From what I know, some of the stories might involve the Game Grumps having funny arguments or debates while drunk. They could be arguing about the best strategy in a game, but because they're drunk, their logic is all over the place and it turns into a really comical exchange. Also, there might be stories about how their drunk state affected their interactions with the games' characters or levels in unexpected ways.
The 'Game Grumps Drunk Stories' could potentially have tales of them trying out new games while drunk. They might start playing a game that they thought was simple but in their drunken state, it became a huge challenge. For example, they could be playing a racing game and instead of following the track, they end up driving all over the virtual place, crashing into things and laughing hysterically. And perhaps there are stories about the strange things they said during the gameplay too, like coming up with really out - there theories about the game's plot or characters.