I don’t think I need to explain it that much. Ordering drinks at the poker table and making them visible for all players just for RP reasons seems like a quite simple feature increasing the casino feeling a lot 
Maybe just add a key to consume the ordered drink.
This reminds me of a game I played a number of years ago. It was called Hoyle Casino 2004 if i recall correctly. Occasionally through poker games, the game would offer you to buy drinks and whatnot. NPCs could also buy them, and you could click on yours to drink it. The NPCs would also occasionally drink theirs. I don’t think it was done for any changes to gameplay, but it was a nice touch. So, even though I don’t play poker in this game, I think it’d fit well enough. Maybe just keep people from vomiting though, or having intense screen effects when they drink so much, could be distracting otherwise.
It should change the gameplay, otherwise you’re going to have people in there throwing up all the time in addition to mic spamming. If they’re going to throw up on me, I want them to not be able to see straight enough to comprehend their cards.