Yeah... probably any definition is going to fall down at some point, >_<.
Granted, Chess's imperfect information is related to the number of potential moves and directions a match can take from any given point going forward, and not knowing what the opponent will take, as opposed to 'hidden' information like cards in a player's hand.
But, I realized after posting that definition wasn't going to hold up in all cases. ^_^;
I think there's a point where a thing isn't a game... like an artificial heart isn't a game, for sure, but that doesn't mean there's an easy-to-agree-upon border between game and non-game. {shrug}