I don't think violent FPS is the cause of that particular type of crime. FPS (multi-player, at least) is simply making a normal game children play digitized.
(I don't know how many of us can remember the arguments over "I shot you!" "No, I shot you first!" "You couldn't shoot me, you were already dead!" Well, the FPS games solve those arguments.)
Games like GTA and the like that glorify violence, crime, and murder are often pointed to as well. They also aren't the cause, they are just a reflection of what our society has become.
Video games, taken singly or as a whole, are not responsible for any crimes in the country. (Now, arguing about them as a part of the instant-gratification dopamine feedback that encourages far too much unproductive time-wasting, especially in young men, may be useful, but that's not about crime.)
The problems in our country are deep-seated and are, at worst, exacerbated by our technology, not caused.