I'm no historian, but having studied Dante and the 12th to 14th century quite extensively, I do believe that I can give a satisfactory answer.

With an estimated 500 000 contemporary speakers, you are completely right in saying that nowadays, Occitan is an almost insignificant language, but its influence during the medieval period was extremely strong especially in the litterary field through the troubadours.

Though ususally translated as jesters in english, the historical troubadours were actually very far from your lowborn fool in bright attire making an idiot of himself in front the local lord. First of all, troubadours were nobles, sometime very high in the hierarchy, such as Guillaume IX d'Aquitaine, or even Richard Lionheart, who could be counted as a troubadour considering his works in occitan language, it was obviously not his main activities, but nonetheless. Now what the troubadours mainly did was poetry, especially in what was called fin'amor, a genre which emphasized chivalry and more importantly courtly love. Usually, the troubadour had a lady for whom he sang his songs and poems to seduce her and though love and its expression were central in that, for the most part, there was no actual sexual relation. There was even the ultimate trial, the ultimate proof of love, the "assag" where one would sleep next to his beloved without doing anything. I'm slightly sidetracking from the main question, but you can see how influencial fin'amor was on Dante's own conception of love, with Beatrice who he reportedly only saw twice in his life and stayed his muse throughout his life.

Now the troubadours were without any doubt the most renowned writers of their times and it peaked under the reign of Alienor of Aquitaine, hence why Richard I can be counted as a troubadour. Without a doubt the most important woman of the time, Alienor was in possession of pretty much half of France, bringing her enormous wealth and power and thus enabling her to protect and finance all the troubadours. Eventually, these troubadours will influence pretty much all of western litterature thanks to the pretige of Alienor's so called Court of Love. They will most notably influence French Litterature in Oil language, mainly thanks to the court of Alienor's daughter, Marie de Champagne, who protected writers such as Chrétien de Troyes, who is by far the oldest french litterary figure that is still largely known and studied today and though he didn't write in Oc, the themes of chivalry and courtly love have a significant place in his works.

The point I'm trying to make is that the troubadours were of unmeasurable litterary influence in the 12th century and one could even argue that they birthed "modern" litterature but as I'm no litterature expert, I'll refrain to claim such a thing.

Dante was born right after this peak of Occitan litterature, its influence deminished, but still very much present and Dante's admiration for the troubadours can be found in several of his works and writings where he praises them, in De vulgari eloquentia, he mentions Bertran de Born, Arnaut Daniel and Giraut de Bornelh as the best poets in their categories (war poetry, love poetry, moral poetry).

But his admiration also stems from the fact that the troubadours were writing in vernacular tongue, something that, seems normal for us, but until then, it was still latin that was the language of litterature. For Dante, that is extremely important, because a huge part of his litterary enterprise was to unify the "Si" language (a term inspired by the Langue d'Oc and Langue d'Oïl) at a time where Italy was extremely divided, both politically and linguistically, so naturally, poets writing in vernacular tongue and becoming renowned throughout Europe could only be a source of inspiration for a man who wanted to (and did!) birth a unified italian tongue.

Now as to why Occitan declined, the main factor would be the birth of a modern administrative system in Oïl. That does not only come from the Revolution, though that was fondamental in the process, it starts from the 100 years Wars and slowly continues as François Ier proclaims the use of French for royal decree, as the birth of absolutism forces everyone in the high aristocracy to move to Versailles and use Oïl etc and what killed regional languages was the creation of the modern school under the Third Republic which violently punished any pupil using their regional language.

The albiegean crusade wasn't that detrimental in the process. The albiegean crusade, despite its name, was mainly a political war, proof is, the French Kings only got involved when they were offered by the Pope to directly rule over the conquered land. The number of heretics have been largely overestimated for some time, with only 20% of the region actualy converted to catharism and that mainly affected low-nobles and low-borns, the counts of Toulouse, ruling over the land, never converted and were only guilty of innaction. Furthermore, the areas of the Crusade, while Oc-speaking, weren't at all in the more culturally significant areas, the Occitan courts were rather in Poitiers and Bordeaux, not Toulouse, Béziers or Alby. So really, I'm rather circumspect regarding the claims in the video, maybe she has information that I don't, but to me, she consderably overestimates the link between troubadours and the Cathars, especially considering the fact that the Crusade and the spread of the heresy happened after the peak of the troubadours. Also, what really sets up red flags to me, is when she talks about what are now called the Cathar castles. These weren't built before the crusade, they were called bastides and they were built after the crusade and were part of a greater anglo-french rivalry regarding Aquitaine. If anything, it's rather that conflict that marked the end of the troubadours, engulfing the (almost) entire Oc-speaking region in a two-century long conflict, during which the nobles had better thing to do than poetry and the region lost the unity and power that it had under Alienor, divided between two much bigger players.