Im gonna be honest, ive seen people saying this game should implement multiplayer but I dont think this format fits well with pvp style. There's just too much advantage for the starting player and honestly the fact that you are fighting against the dealer AI is what makes this game stand out. Making this game one of those pvp game with rewards and ranks would ruin the game's perfect atmosphere of isolation and desperation in my opinion.
As much as I think multiplayer could be fun, I think you are unfortunately right. If nothing else it would require a lot of thought and really good atmosphere but at the end of the day it would more than likely fall short in some way. Could still be really cool, but very hard to do and still keep the experience full.