I see where you're coming from, but the majority of competitive games have a large element of modeling your opponent and predicting his actions. Without playing this one, it seems pretty silly to advertise it as exceptional.
Most games give you one chance at estimating your opponents subjunctive decision theory. If I understand this one correctly, it involves a lot deeper probing of their decision theory. This has significant differences from regular "predict the opponent" game mechanics in that you have to build up a strategy that works even when the opponent knows it (and knows that you know that they know ...). So it seems like the emphasis is unique, and matches the kind of reasoning we've talked a lot about here in the context of newcomblike problems.
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.