I think its a neat idea.
It occurred to me that using either webhooks or a plugin which fires on the post_created event would allow you to interact with an api (and maybe apis for more well-known games like chess or tic tac toe already exist) that could be called and respond accordingly with game state, or written in the programming language of your choice etc.
That way
A. Your discourse instance isnt storing game state
B. You could have multiple ‘clients’ other than discourse, so people could play by email or WhatsApp or whatnot.