CARSON (turning to KEITH): Keith, would you like a cigarette? Here, this is a particularly rational brand.
KEITH (a bit bemused): "Rational...?" (A slight pause) Oh, I'm sorry, thank you. I don't smoke.
(Exclamations of disapproval from JONATHAN and GRETA.)
GRETA (lashing out): You don't smoke! Why not?
KEITH (taken back): Well, uh... because I don't like to.
CARSON (in scarcely-controlled fury): You don't like to! You permit your mere subjective whims, your feelings (this word said with utmost contempt) to stand in the way of reason and reality?
-Mozart Was a Red: A Morality Play In One Act, by Murray Rothbard
Disregarding for the moment the question of whether video games are a rational use of one's time:
Frozen Synapse is a turn based strategy combat game that appears to be particularly interesting from a rationalist standpoint. I haven't played it, but according to the reviews, it's actually a combination of turn-based and real-time play. Each turn encompasses 5 seconds of realtime, but that 5 seconds of realtime doesn't happen until both players have constructed their moves, which they may take as long as they'd like to do. Constructing a move involves giving your several units and your opponent's several units commands, watching what happens when the units play out those commands, and repeating that process until one has a set of commands for one's units that one considers optimal given what one predicts one's opponent will do. This happens on a procedurally-generated battlefield; there are reports of this occasionally giving one player or the other an insurmountable advantage, but the reviews seem to indicate that being able to play on a fresh field each time and having to think about proper use of its layout on the fly outweighs this issue.
Also, the game came to my attention because there's a Humble Bundle available for it now, which means that it can be acquired very nearly for free; just ignore the 'beat the average to get more games' hook.