Sunday or Saturday?

Like a great many of us, and in fact all of us, no one gets it all right. The video you linked is half right, and half wrong. The church dogma does not understand prophesy very well, and has a hard time trying to harmonize the scriptures. The establishment church dogma of future prophesy is wrong because they do not understand the language of prophesy.

But, then neither do the churches that worship on Saturday.

Point 1:
Because of the Julian and Gregorian calendars how do we know today which day is the 7th day, and which day is the 1st day of the week? There are some who are trying to recalculate the days of the week based upon a Hebrew method of counting from the new moon siting. See here

Point 2: It is necessary to study the language of prophesy in order to understand God's judgment language. He used several key elements repeatedly in many of them. They are metaphors which may have had literal fulfillment, or were other times symbolic of the actual events that occurred.

The stars of heaven were most often the tribes / children of Israel. The promise God made to Abraham is the key:

" that blessing I bless thee, and multiplying I multiply thy seed as stars of the heavens, and as sand which [is] on the sea-shore; and thy seed doth possess the gate of his enemies;" Gen. 22:17 (YLT)

If used in prophesy / judgment of other nations, the stars stood for lesser ruling authorities such as princes or provinces under a king. See Isa. 13:10 discussing the fall of Babylon.

In judgment language, "earth" was most often the land of Israel. "Shaking the heavens" was an overturn or fall of a nation or kingdom. Suns were kings, moons were queens or lesser rulers. Earthquakes, melting mountains, lifting valleys were all metaphors that spoke of a nation's downfall.

You have to let the scriptures define the scriptures. Look for the metaphor words "as", "is", and "are", or "like". These will tell you what God is using to equate one thing with another. I have pin pointed many of the OT scriptures for the prophetic judgment language in a series at my blog on The Signs of Revelation, Parts I - VIII at ShreddingTheVeil which you might find helpful.

Point 3: Christ fulfilled all of the law (Matt. 5:17). He did not fulfill just some of it, or only part of it. He fulfilled ALL of it. Each of the feasts, every high sabbath, every regular sabbath rest were all pointing to Christ. The Sabbath rest is now found in Christ (Heb. 3:18; 4:1, 4,10).

The sabbath was for man, to remember and focus upon God, to fellowship with God, and to be restored / strengthened in His word. See. Ex. 20:8-11; 31:13-16; Lev. 23:15-16; etc.

You might like to read the information here about how Christ fulfilled the OT feasts.

Point 4: That Christ walked part way with the two disciples on the way to Emmaus (Luke 24:13), which was 60 furlongs (about 7 miles) from Jerusalem on the day He was resurrected just about kills the idea of a sabbath resurrection. The two disciples would not have considered walking that distance on a sabbath day.

Point 5: Pentecost was on the first day of the week, the day after the 7th regular sabbath. (Lev. 23: 15-17). Christ's church was established on Pentecost, the first day of the week (Acts 2:38-41).

When we are baptized into Christ (immersed into His name), we have entered His rest, and we are His. We are to live our lives as His ministers, praying continually (1 Thess. 5:17; Col.3:17). We are His royal priesthood (1 Pet. 2:9). Our sacrifices are the fruits of our lips (prayers and teaching) and our good works (Heb. 13:15-16).

Whenever we meet - whether on Saturday, Sunday, Wednesday, Monday morning - we are in fellowship with one another and with Christ our Lord and Savior, and we are in His rest, His Sabbath.

Matt. 11:28-30,

"28 `Come unto me, all ye labouring and burdened ones, and I will give you rest,

29 take up my yoke upon you, and learn from me, because I am meek and humble in heart, and ye shall find rest to your souls,

30 for my yoke [is] easy, and my burden is light.'" (YLT)

Further reading:

Why Jesus Christ Has Become Our Sabbath Rest here

True Sabbath Rest Through Christ here

All bold emphasis is mine.

Adding to @SLM's answer, you have passages like Luke 18:12 where the Pharisee says that he fasts δίσ του Σαββάτου, which makes little sense if you think he's fasting twice per Saturday. C.f. BDAG.

Colossians 2:16-17 makes explicit that keeping the Sabbath is no longer a binding commandment in Christ. " Let no man therefore judge you in meat, or in drink, or in respect of a feast day or a new moon or a sabbath day: which are a shadow of the things to come; but the body is Christ's."

The translation is correct that in Acts 20:7 they gathered on Sunday. We know this for a number of reasons, but clearly because the same phrase and words are used at John 20:1, 19 in regard to Sunday the first day after the Sabbath.

Acts 20:7 μιᾷ τῶν σαββάτων

John 20:1 μιᾷ τῶν σαββάτων

John 20:19 μιᾷ τῶν σαββάτων

We know the events of John 20:1 and 20:19 took place on a Sunday. The women visit the tomb and find it empty. Later that same day (Sunday), Christ Jesus appears to the apostles.

PS. Please don't worry that the mark of the beast is somehow related to worshiping the Lord Jesus Christ on Sunday, the first day after the weekly Sabbath.