Actually, most of those studies have been disproven when accounting for other factors. Killing people in video games isn't usually like killing a real person; it's merely an obstacle in the way. As video games got more "realistic" they needed more realistic enemies. I don't think kids ever fantasized about killing turtles because they played a lot of Super Mario Brothers. Frankly, I remember playing with army men as a kid, and pretending I was shooting bazookas, guns, etc etc. It's a matter of scale rather than kind.
And in 99% of video games, you're not killing "innocents". GTA is a notable one, but there's not many others that are mainstream. Most usually involve killing "bad guys".