The idea is that the game code is running on the blockchain itself (not the rendering to cute kitties though), so there is no game server that can be shut down by the developers. So even if the game stops being profitable and the devs lose interest, the game could presumably keep going and everybody would still have access to their kitties and trade them.
(except in this case there is a self destruct function that would freeze the game forever)
(except in this case there is a self destruct function that would freeze the game forever)