Has there ever been a true kidnapped princess from anywhere in the world?

Adelaide of Italy inherited the Kingdom of Italy when her husband, Lothair, died. She was captured by Berengar II of Ivrea, who aspired to the crown. An account of this was written by her biographer and acquaintance, Odilo of Cluny, one of the most powerful people in Europe at the time. When she refused to marry Berengar's son, Adalbert, she was imprisoned. She escaped after three months to the Castle of Canossa (later famous for another regent, Matilda of Tuscany). Berengar II unsuccessfully besieged her in this castle for three years. She sent an emissary to Otto I for protection. She met Otto in Pavia in 951 and they married, making her the empress of the Holy Roman Empire. She was beatified in 1097 by Urban II.

The kidnapped princess is an example of the damsel-in-distress theme in adventure stories. The hero of the story saves the female from peril and then marries her. Another representation of this theme was the princess and the dragon, where the princess was abducted by a dragon.

As a nuance to your question, nobles and others were frequently married against their will.

Here is a near miss: Julia Gonzaga.

In the night of 8–9 August 1534, the town of Fondi was attacked by the corsair Barbarossa, who was seeking to kidnap her and deliver her to Suleiman the Magnificent, his emperor. Barbarossa had been ordered to kidnap her by Ibrahim Pasha, the Ottoman Grand Vizier. Pasha's plan was to add her to the sultan's harem and supplant Roxelana, the sultan's wife. She escaped, and Barbarossa, frustrated, massacred the populations of Fondi and nearby Sperlonga, though he was repulsed at nearby Itri. She fled into the night, accompanied by a single knight. She later had the knight killed because she had been nearly nude during her escape and he had seen too much.

And more generally:

Bride kidnapping, also known as marriage by abduction or marriage by capture, is a practice in which a man abducts the woman he wishes to marry. Bride kidnapping has been practiced around the world and throughout history. It continues to occur in countries in Central Asia, the Caucasus region, and parts of Africa, and among peoples as diverse as the Hmong in Southeast Asia, the Tzeltal in Mexico, and the Romani in Europe.

In the Norse sagas there are a few examples, such as Eyfura, who bore the twelve sons of Arngrim the Berserker.

According to the Hervarar saga, versions U and H, she was the daughter of Svafrlami, the king of Gardariki. Her father was slain by Arngrim who took Eyfura as his wife by force.

And Rind, who bore Vale, destined to avenge the death of Balder.

The most detailed account is in Book III of the Gesta Danorum, written by Saxo Grammaticus around the early 13th century. There she is called Rinda and is the daughter of the King of the Ruthenians. After Balderus' death Odin consulted seers on how to get revenge. On their advice Odin went to the Ruthenians disguised as a warrior called Roster. There he was twice turned down by Rinda. He then wrote runes on a piece of bark and touched her with it, causing her to go mad, and disguised himself as a medicine woman called Wecha, who was allowed to see her. Finally she fell ill; the disguised Odin then said he had medicine with which to cure her but that it would cause a violent reaction. On Odin's advice, the king tied Rinda to her bed, and Odin proceeded to rape her.

Nest ferch Rhys was the only legitimate daughter of Rhys ap Tewdwr, the last king of Deheubarth in Wales, so she was certainly a princess. She was raped and abducted in 1109 by Owain ap Cadwgan, but was eventually returned to her husband.

The four daughters of Nicholas II of Russia, Olga, Tatiana, Maria and Anastasia were captured by the Bolsheviks and held prisoners. They were murdered on July 17th, 1918 in Yekaterinburg, even though they were all completely innocent of their father's crimes.

I know technically they did not hold the title "Princesses", but "Grand Duchesses" (which is a higer title), but I don't think this is important to the question.

The Sabine Women might qualify

Consequently, the Romans planned to abduct Sabine women during a festival of Neptune Equester. They planned and announced a marvelous festival to attract people from all nearby towns. According to Livy, many people from Rome's neighboring towns attended, including folk from the Caeninenses, Crustumini, and Antemnates, and many of the Sabines. At the festival, Romulus gave a signal, at which the Romans grabbed the Sabine women and fought off the Sabine men. The indignant abductees were soon implored by Romulus to accept Roman husbands.2

I'm not sure why OP rejects Mary Queen of Scots

James Hepburn, 4th Earl of Bothwell, was generally believed to have orchestrated Darnley's death, but he was acquitted of the charge in April 1567, and the following month he married Mary. Following an uprising against the couple, Mary was imprisoned in Loch Leven Castle. On 24 July 1567, she was forced to abdicate in favor of James VI, her one-year-old son by Darnley. Wikipedia

(most of the stuff I've read indicates that her marriage to Bothwell was not voluntary; she was kidnapped and raped).

Boadica may qualify

Boudica's husband, Prasutagus, ruled as a nominally independent ally of Rome and left his kingdom jointly to his daughters and the Roman emperor in his will. However, when he died, his will was ignored, and the kingdom was annexed. According to Tacitus, Boudica was flogged and her daughters raped.4

And arguably Anne Neville

More important, he married Warwick’s youngest daughter, Anne Neville, widow of Edward of Lancaster. There is no need to suppose that this was a love match, for he insisted on her share of her parents’ immense inheritances in a bitter dispute with his brother George, husband of the elder daughter. The three royal brothers colluded in depriving the countess of Warwick of her entitlements, more than half of the whole.

My professional historian girlfriend suggests (somewhat tongue in cheek) Patty Hearst - because in America "princess" is a loose term. I've lost track of the number of teachers who argue that "celebrity" is equivalent to "nobility" at a minimum.

Slightly less tongue in cheek, I'd challenge the question; take for example Caroline of Brunswick, who was shipped off to a foreign land to marry a Prince. The decision was made against her will (arguably; she'd never met the man). Most royal women were the instruments of foreign policy, not participants. Kidnapped princesses were the norm, not the exception.

I just re-read the question and noticed that OP is looking for a military operation to seize a princess. I'd argue that Boadica still applies - the Roman's invaded the Isceni lands to seize the women. Mary Queen of Scots should still qualify - although technically it can't be a "military" operation, since both Bothwell and Mary employed Scottish troops. I'd argue that in most cases in both history and fiction, a military operation to seize a person is rare - a covert op is much more plausible. If you're going to exclude cover ops and police operations, then the question becomes artificially narrow.

Eleanor, the Fair Maid of Brittany (c. 1184-1241) The daughter of Geoffrey II, Duke of Brittany and sister of Arthur of Brittany (1187-1203) was the rightful heiress of England, Brittany and other Angevin lands after the mysterious death of her brother, and was imprisoned by King John and by Henry III until her death.

Bu there is no record of how King John gained possession of her person, and so no proof that she was technically kidnapped.

Duke Bretislav I of Bohemia (1002/05-1055) kidnapped his future wife Judith of Schweinfurt (before 1003-1058) daughter of Margrave Henry of the Nordgau, from the nunnery in Schweinfurt in 1019. Their children included Duke Vratislaus II, who became the first King of Bohemia. Neither of the families was of royal rank, but the original question does not specify royal princesses, and both families were certainly of princely rank.

Emperor Lothair I's children included had a daughter and princess who was kidnapped and married in 846 by Giselbert Count of the Maasgau.

I believe there are a number of other historical examples I can't think of at the moment.

Galla Placidia makes an early example of kidnapped princes marrying her captor.

Galla Placidia was daughter of Roman emperor Thedosius I and half sister of emperors Arcadius and Honorius. When Visigoths sacked Rome in 410 she was made captive by king Alaric. A couple of years later, she married Alaric's successor Ataulf.