I don't really want to get into an arguement about this, but I'll trhow in the standard corelation is not causation line, with the correlary that lack of correlation does not imply lack of causation. In fact, people who do make arguements out of crappy pseudo-statistics like this should be shot
.
The fact that violent crime dropped at the same time video games were introduced and rose in popularity is no evidence that video games do not cause violence. It's a problem of couterfactuals. Maybe without video games, violent crime would have fallen at a lower rate. Maybe without video games violence would have fallen at a faster rate. Maybe there is no link. With so many intervening variables this correlation means nothing. The fact that youth violent crime is at historically low rates does preclude the possibility that violent video games cause many violent acts.
I'm not really familiar with the literature on this stuff, but it seems to me that the best way to isolate these effects is experimental lab studies. Some of these have found a link between violent video games and violent behavior:
http://www.apa.org/releases/videogames.html
(.pdf of the actual journal article)
http://www.apa.org/journals/features/psp784772.pdf