Are countries with other religions doomed for hell?

The first couple chapters of Romans speak to your concern I believe. There Paul quotes the old testament when he says God:

“will render to each one according to his deeds”: eternal life to those who by patient continuance in doing good seek for glory, honor, and immortality; but to those who are self-seeking and do not obey the truth, but obey unrighteousness—indignation and wrath

I generally understand the opening passage as an appeal to judgemental Jews who believed that they had a special claim to salvation. In this day I believe it applies to Christians who only believe their nation/denomination/group will receive grace.

There is a story in the Bible, told in 2 Kings 5, that can help us understand this question. The story is that of Captain Naaman, an officer of high rank in the Syrian army. He was not an Israelite, and was not a God-worshiper; but he had the fortune of having acquired a maid-servant, a young girl, brought captive from Israel. This little girl was able to give him hope when the doctors in his country diagnosed him with leprosy.

In those days, leprosy (now often called Hansen's disease), was incurable. Being contagious, and leading to a miserable death, lepers were forced to leave their family and society and dwell alone or with other lepers. So Captain Naaman's condition was very serious. But the little maid who worked in his home gave him hope, telling him that he could find help in Israel at the hands of the prophet in Samaria. She told the captain's wife that the prophet would be able to heal him. This news was then carried by others to Captain Naaman himself. The record implies that the king heard this exchange--perhaps Naaman was in the king's presence when the news reached him--because the king, not wanting to lose his captain, then sent him with a letter to the king of Israel to seek out this healing--along with "ten talents of silver, and six thousand pieces of gold, and ten changes of raiment."

The king of Israel was shocked to receive a Syrian who had come to ask for healing from leprosy. He was not a prophet, and lacked the prophet's faith. "Am I God, to kill and to make alive, that this man doth send unto me to recover a man of his leprosy?" he responded.

But the prophet Elisha heard about this, and sent a message to the king of Israel, saying, "let him come now to me, and he shall know that there is a prophet in Israel."

Naaman went to Elisha. Upon arriving, he was given a message from Elisha's servant--Elisha did not see Naaman himself. The message was to wash in the Jordan River seven times. Naaman, perhaps offended at not seeing the prophet himself, and being told to wash in the muddy waters of the Jordan, would have return straightaway to Syria had his servants not persuaded him to go ahead and try, as it was but a small thing that had been asked of him. Naaman listened to them, and went down to the river and washed himself seven times. The leprosy was healed. He was clean!

With joy he returned to Elisha. Captain Naaman then says: "Behold, now I know that there is no God in all the earth, but in Israel: now therefore, I pray thee, take a blessing of thy servant."

The captain then offered his gifts, but Elisha would not accept them. The prophet wanted him to know that it was not Elisha the Prophet who had healed him, but the God of Heaven. The captain then says something quite interesting, to which Elisha makes no argument.

In this thing the LORD pardon thy servant, that when my master goeth into the house of Rimmon to worship there, and he leaneth on my hand, and I bow myself in the house of Rimmon: when I bow down myself in the house of Rimmon, the LORD pardon thy servant in this thing. (2 Kings 5:18, KJV)

Elisha says simply: "Go in peace."

Was this permission for Naaman to bow to the idol in the temple of Rimmon? Perhaps not, but neither does God see fit to prohibit him in this thing.

In 1 Samuel 16:7 God says:

. . . for the LORD seeth not as man seeth; for man looketh on the outward appearance, but the LORD looketh on the heart. (1 Samuel 16:7, KJV)

God is not looking so much at what we do as at why we do it. What was in our heart? What motive prompted our action? There are many people in "heathen" lands who have not heard about the true God. But God will look at their hearts to see if they are living according to the good that they know. Are they selfish, or unselfish? Are they kind, honest, and true to principle inasmuch as they have understanding? or are they seeking to cheat others, take advantage, and bend the rules wherever possible? Do they do what they believe to be right, or do they try to excuse themselves and rationalize their wrongs?

There are many who do not know God whom God will save. They have done their honest best. They did not know all of the truth, but the followed all of the truth that they had. However, the more truth we know, the better able we are to choose the path of truth. Christians are more privileged than those who are ignorant of God; and this is why they have the responsibility of sharing their knowledge with those who are less privileged.

Are countries with other religions doomed for hell?

The short answer is no.

I say unto you that likewise more joy shall be in Heaven over one sinner that repenteth, than over ninety and nine just persons who need no repentance. - Luke 15:7

God certainly desires the conversion of all nations to Christianity. As God enjoys the conversion of individual sinners that my have eternal life; the same holds true for entire nations.

Armenia is the first historical name nation to become Christian in 301 A.D. and it is celebrated with great pride in Armenia.

Celebration of the Feast of Holy Etchmiadzin

On Sunday, June 10, the worldwide Armenian Church and nation celebrated the Feast of the Universal Church of Holy Etchmiadzin. The annual celebration commemorates the founding and establishment of the mother cathedral of the Armenian people in 301 A.D. The preceding day, the Armenian Church celebrated the *(Deliverance of St. Gregory the Illuminator from the Pit**, which commemorates the patron saint’s liberation from the deep dungeon and the beginning of the conversion of the noble house of Armenia to Christianity.

In the Mother See of Holy Etchmiadzin, the feast was commemorated with the celebration of a special Divine Liturgy, presided over by His Holiness Karekin II, Supreme Patriarch and Catholicos of All Armenians. His Grace Bishop Arshak Khatchatrian, Chancellor of the Mother See, celebrated the liturgy.

On Saturday, during Evening Services, the relics of St. Gregory the Illuminator were placed in the center of the Cathedral next to the Holy Altar of Descent, and were venerated by the faithful throughout the night, into the next morning and throughout the day of the feast.

The Armenian Apostolic Church is the national church of Armenians. It is part of Oriental Orthodoxy and is one of the most ancient Christian institutions. The Kingdom of Armenia was the first state to adopt Christianity as its official religion under the rule of King Tiridates III of the Arsacid dynasty in the early 4th century. According to tradition, the church originated in the missions of Apostles Bartholomew and Thaddeus of Edessa in the 1st century. St. Gregory the Illuminator is the first official primate of the church.

Gregory is revered as the patron saint of the Armenian Church. He is recognized and memorialized in both eastern and western hierarchical churches. The Armenian liturgical calendar reserves three feast days in his honor: Entrance into the pit; deliverance from the pit, and discovery of relics. In addition to these three days, there are several feast days to which he is closely connected, namely the feast days for Sts. Hripsimiantz, Sts. Gayaniantz, Shoghakat, Holy Etchmiadzin, and King Trdat. The Roman Catholic Church, Orthodox churches, and Oriental Orthodox churches have special days in their calendars for the veneration of St. Gregory, who is considered to be one of the Fathers of the early Christian church.

Gregory was condemned to the pit in 287 AD by King Trdat and the persecution of Christians began. After the martyrdom of a group of nuns who came to Armenia from Rome led by Hripsime and Gayane, Trdat was stricken with strange maladies. His sister, Khosrovidukht, had a dream that Gregory was the only person who could heal her brother. Miraculously, Gregory was still alive after many years in the pit, thanks to the daily visits of an angel. Gregory emerged from the pit; the king was healed and baptized, and he declared Christianity to be the official religion of Armenia.

Gregory was not the first to preach Christianity in Armenia. That distinction belongs to the apostles Thaddeus and Bartholomew who came to Armenia in the first century, and thus gave the Armenian Church its apostolic designation. Nevertheless, Gregory is revered and is considered by Armenians to be the father of their faith. Hundreds of churches have been built and named in his honour. - Feast of St. Gregory the Illuminator: Deliverance from the Pit

Let us recall this is the Land of My. Ararat, the Land of Noah's Ark!

You shouldn't have such an absolute and depressing view of God's justice. This is a common cause of anxiety among all of us who convert, as we think of what happened to our beloved family members who died without God. This kind of doubt only happens after we are fed the antichrist misconceptions about Christianity. The standard view of certain wicked Jews about Gentiles was that they were created as fuel of hellfire (unfortunately, the Gentile Christians began to believe the same about all who die unbaptized, even the infants, on the basis of original-sin doctrine). Jesus condemned such doctrines of those who thought their religion or ancestry alone saves them by default. See Matt 3:7-9. The whole teaching of Christ was to rebuke the misconception that faith alone can save you and that works doesn't matter. The parables of The Good Samaritan makes it abundantly clear, that a righteous heretic or pagan will be counted righteous, but a sinful high priest will be condemned for his failure. The same was already taught throughout the scriptures.

Apostle Paul calls this a mystery, that the gentiles are fellow heirs of the promise, and one body with the Jewish church/religion through the Christian gospel. A mystery, because it comes as a surprise to the Jews. Paul explains that a Gentile is counted righteous when he does the works of the law (basic moral requirement, or the fundamental crucial requirements of the law) through his conscience. Romans 2 is the key chapter for this topic. Rom 2:5-16 NJB:

Your stubborn refusal to repent is only storing up retribution for yourself on that Day of retribution when God's just verdicts will be made known. He will repay everyone as their deeds deserve. For those who aimed for glory and honour and immortality by persevering in doing good, there will be eternal life; but for those who out of jealousy have taken for their guide not truth but injustice, there will be the fury of retribution. Trouble and distress will come to every human being who does evil -- Jews first, but Greeks as well; glory and honour and peace will come to everyone who does good -- Jews first, but Greeks as well. There is no favouritism with God. All those who have sinned without the Law will perish without the Law; and those under the Law who have sinned will be judged by the Law. For the ones that God will justify are not those who have heard the Law but those who have kept the Law. So, when gentiles, not having the Law, still through their own innate sense behave as the Law commands, then, even though they have no Law, they are a law for themselves. They can demonstrate the effect of the Law engraved on their hearts, to which their own conscience bears witness; since they are aware of various considerations, some of which accuse them, while others provide them with a defence . . . on the day when, according to the gospel that I preach, God, through Jesus Christ, judges all human secrets.

A few Church leaders after the third century understood these basic facts about God's impartial justice, that he will judge all equally. Chrysostom writes in the fifth century:

Conscience and reason take the place of the law. By saying this, Paul showed that God made persons independent, giving them the freedom to choose virtue and avoid vice. Do not be surprised that he proves this point, not once or twice but several times. He had to do this in order to counter those who said: “Why did Christ delay his coming so long? Where was this great scheme of providence before Christ came?” … But even before the law was given the human race enjoyed the care of providence. Why does Paul insert the words accuse or perhaps excuse? If they have a written law and do what it says, how can their thoughts still accuse them? Paul is not speaking here of the righteous only but of all mankind. For then our thoughts do pass judgment, some excusing us and others accusing. And at that tribunal, one needs no other accuser.

Nations around the world, before Christ or today, don't have an unfair hindrance to God's justice for not having been preached about God; the unevangelised and even those ill-evangelised by false Christians. God applies the atonement of his blood for the forgiveness of gentiles despite dying without consciously embracing Christ, according to the top Christian philosopher, Dr. Craig of reasonablefaith, however, being a traditional Christian, he thinks that such people may be very few who gain the providential grace of God. "No Other Name": A Middle Knowledge Perspective on the Exclusivity of Salvation Through Christ:

Nor does it seem to me that the problem can be simply reduced to the inconsistency of a loving and just God's condemning persons who are either un- , ill-, or misinformed concerning Christ and who therefore lack the opportunity to receive Him. For one could maintain that God graciously applies to such persons the benefits of Christ's atoning death without their conscious knowledge thereof on the basis of their response to the light of general revelation and the truth that they do have

You should be therefore, be confident about God's perfect justice. God sends rain and sunlight on all his creation impartially. He will punish the bad, and he will not withhold the rewards earned by the righteous. All who do righteous works will earn life, or salvation.

[Rev 22:11-12 NJB] Meanwhile let the sinner continue sinning, and the unclean continue to be unclean; let the upright continue in his uprightness, and those who are holy continue to be holy. Look, I am coming soon, and my reward is with me, to repay everyone as their deeds deserve.

[Acts 10:34-35 NJB] Then Peter addressed them, 'I now really understand', he said, 'that God has no favourites, but that anybody of any nationality who fears him and does what is right is acceptable to him.

The Israelites were a nation whose fortunes grew or declined as the society as a whole did or did not follow God's rule. The people were collectively chosen to serve as an example (both good and bad) to the rest of mankind.

But Christians are considered to be "spiritual Israel". They too are God's chosen people, but they are chosen individually, not according to their nationality or other attributes:

There is neither Jew nor Greek, there is neither slave nor free, there is neither male nor female; for you are all one in Christ Jesus.
— Galatians 3:28

So, the question "Is that entire country just doomed" is meaningless from the point of view of Christianity.

During this age, God is calling individuals, not nations, to salvation.

If you are really asking what happens to all those individual people that never had a chance at salvation, that is a completely different question, which has already been asked and answered in other questions.