Currently, all game-gamestate variables are just ints. This is not
particularly type-safe, in case the number of enums changes. To verify
that all current uses of the game-gamestate variables actually use the
enums, change them to be typed with the enum instead.
(As an aside, we should probably rename this so that it can't be
confused with Terry's state machine that has several different ways to
exploit to warp you to the credits, but that's something to do later.)