If you want an example of how to write a game with no reward driven play:
Imagine »
No conflict – No game master – No dice or other means that provides random outcomes – No prep – No tangible rewards – No acting-in-character – No fantastic elements – No campaign – No mechanical improvements – No 200+ pages to read only to be able to play the game.
I wanted to make a game that created investment in fiction (immersion, but in story). Had no idea if the game was fun, or (more importantly) how it would be fun … but it was, and created investment in a character in under an hour. You could also play this game by yourself, but I think something will be lost due to the lack of uncertainties that the other participants brings (by how the game wants the group to talk to each other).
I guess The Murder of Mr. Crow, also featured in the link, is a game without tangible rewards. Just a game loop, with instructions, that is continuously repeated.