There is a parallel to draw with Bonapartisme.
- in it’s first sense, it is the political group that supports Napoléon Bonaparte.
- in a broader and more frequent sense, it is the political thinking inspired by Napoléon, i.e. a strong centralized power, based on popularity, and proning excellency.
That being said, that’s a neolgoism that I have never heard or seen before. And a google search to Vercingétorisme gives extremely few results. The extract you quote is in a video-game forum, from a post by someone whose pseudonym is “Vercingétorix”.
In conclusion, I see it as a meaningless play on words, exactly like you could say you are for mitchism.
There is another answer to consider :
In the french Film Asterix et Obélix : mission Cléôpatre, the actor Jamel Debbouze has a hard time saying names correctly, e.g. he says “Astérixme” or “Obélixme”. This became a somewhat popular way of play on words and is still used sometimes.
Vercingétorix using the same root I think this is what the user was trying to mean.
I think in the context you cited, it is simply a mistake and the person meant to write “Vercingetorix”, not “vercingetorism”.
As for what Vercingetorix means (which is not the question, I reckon), it means “Great king of the warriors”.