It should be noted that the worldwide decline in overall violence came about in 1993-1994, which coincides with the release of the original Doom.
In the past 10 years, I have spent literally 10s of thousands of hours playing FPS games. I do so for stress relief. If I'm having a bad day at school or work, it is great to blow off steam by shooting someone in the face on the internet.
Video games don't cause violence, they provide a safe outlet for it.