But it's not about an existing game. You make up your own fantasy world and game.
It's similar to portal fantasy type stories.
Large parts of the story take place within videogames, usually in a VR setting, and the character needs to interact within the game to progress the story.
Fanfiction is playing with other people's worlds.
In LitRPG you don't just create a 'normal' world, but you also have to create a videogame with videogame rules, settings and stuff like that. A lot of LitRPG readers love reading about the stats within the game and how the game works and how the characters can play with or against the gaming elements.
As an author, it's really intense to write as it tends to require multiple spreadsheets of gaming stats and such because readers will catch it if you don't.