I've been a "gamer" all my life, beginning with military board games and going right up through MMORPG's (World of Warcraft being the most recent). I agree with Wilf that "simulation" is probably a more accurate term, though I would suggest "model," at least for certain types of "games."

Like any simulation or model, there are limits to what it can do and there are some things that simply can't be modeled/simulated very accurately. In my experience, those un-modelables are often the human and leadership factors. I think we're all in agreement that those human factors are preeminent in insurgency/COIN, so for that reason alone I think games/models/simulations will have less utility in COIN than, say, naval warfare. In other words, it's easier to simulate hardware than it is to simulate people.