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.