Okay so uhh lemme give this a shot, although I'm hoping an actual scholar on the era will show up and do it better.

First off it needs to be understood that Gustav IV was massively unpopular after losing many territories, most notably Finland which was basically the entire eastern half of the kingdom at the time, and any writings about him after he was deposed tend to be tinged with propaganda. He was one of the few Swedish kings to actually be the target of a damnatio memoriae after he was replaced with the first king of the Bernadotte dynasty, which leaves us with very few contemporar works that might show him in a more positive light.

Whether or not he was actually insane or simply an inept ruler with a poor grasp of political realities is far beyond my knowledge to judge, but I tend to err on the side of caution. Did he truly revile Napoleon so because of religious mania, or because he was born and grew up in an era where monarchies and dynasties were either outright falling, or at least finding themselves on much shakier ground, and what was basically an up-jumped commoner (or near enough from a king's point of view) now declaring himself Emperor of France and threatening all of Europe?

So with that out of the way, the main connection I can find would be here and a few pages onwards. B. von Schinkel's "Memories from Sweden's Recent History", the relevant passages written and compiled by C.W. Bergman, famously criticized for being more dramatic than factual. Text in Swedish, I'm afraid.

It is claimed in this book that Gustav IV came into contact with Johann Heinrich Jung and his writings. Among which was Die Siegesgeschichte der christlichen Religion in which the author applies the prophecies of the Book of Revelation to world history (well, mainly European history). As he reaches his present day, the book then continues to include identifying the Beast (or one of the Beasts - I'm not great at Revelations) as not a literal beast, but a powerful man who will seek "universal domination of all mankind" until christ descends and with his army of white-horséd riders defeats the beast.

So basically identifying a powerful political figure as The Antichrist, more or less. Not exactly a unique phenomenon in history. This idea of course fit very well with Napoleon at the time, and would allow anyone opposing him to cast themselves as one of the white knights of Jesus.

Now did Gustav IV take this all literally? Could be. It could of course also be that even without this prophetic understanding he would have seen good reason to resist Napoleon and French influence. The French revolution would scare any king, and it most certainly seemed to have made an impact on Gustav as his uncompromising defiance against Napoleon could simply be understood as a resistance against a new world order in which old monarchies were being swept away.

As Gustav IV was deposed in a coup by a group of Swedish noblemen (after his father had been killed in a coup by a group of Swedish noblemen), any books written by Swedish nobility on him should probably be taken with a few pinches of salt. The fact that he was then replaced as king with Jean-Baptiste Bernadotte - an actual marshal of Napoleon, although he of course famously turned against Napoleon very quickly once he took the Swedish throne - and that the book in question was published by one of Bernadotte's adjutants, and the relevant parts written by the nephew of said adjutant, with the aim of glorifying the new king and painting him as the vanquisher of Napoleon. The book (or rather the relevant first half of it written by C.W. Bergman) was even at the time criticized for being more focused on dramatic effect rather than being factual.

I am not aware of any first-hand accounts of Gustav IV basing his foreign policy on this interpretation of Revelations, but that's not the same as saying it's impossible. He would neither be the first nor the last leader to do so, but the claim that "Gustavus IV of Sweden's world-view was based on a deranged interpretation of the Book of Revelation" is almost certainly based on the succesful propaganda of the king's detractors, and seems to be oddly certain about a rather murky subject.

From what I can see in Dr. Thomson's Travels mentioned in another comment the tone used about Gustav IV is even more brutal than that of the already questionable work of von Schinkel and Bergman - in whose book it is implied that Gustavus might've made an adequate monarch if not for his obsession with Napoleon. Without a clear source it would seem he has gotten his assesment of the former king from the very people who resisted and deposed him, and it looks to me as if it's suffering even more from the desire to paint a dramatically appealing narrative of "the mad king". That's not evidence against his claims, of course, but it certainly doesn't help it's case.

Edit: To make a long ramble short, there is a historical background to this notion - that Gustav IV found inspiration in Jung's interpretation of the Book of Revelations - so the claim made in the quote of the original post is by no means made up. However it is also very questionable how much of this narrative is true, and claims of his being insane, cowardly and so on show up after he is deposed and during the damnatio memoriae. As such I'd argue that any scholar should be very careful about quoting such writings as were made during this time as truth.

This is the first time I have heard of a world-view based on a "deranged interpretation of the Book of Revelation" for Gustav IV Adolf and a quick scan through my available sources in Swedish does not reveal anything like this.

Gustav IV Adolf was certainly a warm christian, pious and a firm believer that he was an absolute monarch by the Grace of God - in the era of enlightenment, this might certainly be seen as "deranged", but is not that much different from how many other monarchs of Europe viewed their position, or at least claimed it was. Likewise, Gustav IV Adolf, as head of the Swedish lutheran church considered Napoleon antichrist, a position the Russian orthodox church would also take in 1812. Deranged? Perhaps, but Gusav IV Adolf was not very different from his fellow monarchs in this.

When it comes to Gustav IV Adolf, one needs to remember that he and his life was extremely vilified by propaganda produced not only by the enemies of Sweden (such as Napoleonic France and at times Russia and Denmark) but also by the coup-makers against him. in order to justify their own coup, the coup-makers peddled a lot of accusations against the King - among them that he was feminine, that he was unable to sire children, that his father was unable to sire children and that he was the child of the queen's lover, that he was incapable, that he was incompetent, that he focused on theatrics and show rather than anything with real substance. Some of these accusations tied into real situations and rumours of the time. His father Gustav III had problems getting his relationship with the Queen working and had asked his favourite the royal stablemaster (but in a lot of propaganda reduced to a handsome stable hand) the nobleman Adolf Fredrik Munck for advice, to the extent that Munck entered the royal bedchamber and instructed the King on how to proceed. Rumour of course had it that Munck was the real father of Gustav IV Adolf, which was peddled in this propaganda piece (very NSFW). Some of the accusations seem to have been from the personality of his father, Gustav III, who was by historians during the 19th century considered effiminate, using make-up, being fond of theater and dressing up (he was murdered at a costume party after all) and his uncle Duke (later King) Karl (XIII) who was considered unambitious, lazy and mostly interested in intricate ritual in various secret societies popular at the time.

A lot of this propaganda has stood unchallenged into modern times, as the man himself was unable to answer the accusations from exile and descending into an ever-worsening alcoholism and the fact that the next dynasty, founded by Jean-Baptiste Bernadotte (as Karl XIV Johan from 1818, but in reality King in everything but name from being adopted and named Crown Prince by King Karl XIII in 1810) had a vested interest in keeping Gustav IV Adolf, his son Gustav and their supporters far away from the corridors of power. Gustav IV Adolf's son, Gustav, did not die until 1877 and served as an officer in the Austrian army, reportedly had good relationships with the Emperor and was ennobled as "Prince of Wasa" in Austria. The Bernadotte dynasty thus had a vested interest in continuing the propaganda against Gustav IV Adolf and by extension his son, as they could have claims on the Swedish throne.

A lot of the reign of Gustav IV Adolf and his father Gustav III are marked by the prolonged conflict between royal power and the nobility, which had enjoyed unprecedented privileges during the "Era of Liberty" 1718-1772, which had ended with Gustav III's coup d'état in 1772 and many of the nobility believed would return with the murder of the King in 1792 and then with the coup against King Gustav IV Adolf in 1809.

Historian Christopher O'Regan have written two books on Gustav IV Adolf, one on his childhood called "Ett märkvärdigt barn" ("A peculiar child") and one on his reign called "I stormens öga" ("In the eye of the storm") which challenges a lot of the traditional views on the personality, mind, goals and actions of Gustav IV Adolf. As such, they have faced some criticism from other historians, but have also received quite a bit of interest as well.

To separate what is propaganda, myth and reality when it comes to Gustav IV Adolf can be quite hard. But there has been an uptick in interest in the era, and several respected historians have recently published works that go to the original sources and paint an entirely different picture of the King and his era.

O'Regan paints a picture of a King gifted in administration and well in tune with the most recent and modern economical ideas of the time, one that did a tremendous work to get the Swedish economy in order and to reduce the absolutely massive debt and curtail the massive inflation by introducing unbacked paper currency that his father had caused. He also laid the legal groundwork of the land shift and enclosure of the commons which would set Sweden on the course for the agricultural revolution. He also paints a picture of someone stubborn, who bet on the right horse by aligning Sweden with the British, but in the end proved incapable of handling the noble opposition and their sabotage of the war effort against Russia and following coup, causing Sweden to lose Finland after 600 years.

The bottom line is that I would assume that section would be based on older historical works from the late 19th century which were based a lot on the propaganda against King Gustav IV Adolf, and not on the more recent research made by historians challenging that view.