No. I think a lot of the talk about video game and movie violence tends to be what we normally see in these situations: people looking for their "devil". What I mean by this is that when people don't understand something, they strive to find a reason, and they tend to be huge proponents of Occam's Razor in that they seem to settle on surface-level answers. In this situation, they see that a kid plays violent games and acts violent in return, so there must be some sort of correlation.
My take is that there is something inherently wrong with the people in question. As to what EXACTLY it is... honestly, I don't know. However, it manifests itself as a lack of empathy and critical thinking that makes them think that taking out whatever frustrations they have out on others in extreme ways as an acceptable thing. In turn, I think their game playing or what could be seen as excessive game playing is likely another symptom of whatever is wrong with them. These kids tend to be disturbed in some way, and usually, a video game serves as a mental escape to get away from problems.
I see people talking about being desensitized to violence, and I'm not sure about that either. From my own personal standpoint, I've been playing violent games for a long time, and I still feel queasy at the sight of gore. Last night, I was watching Red Letter Media's review of Annihilation, which they showed a scene of opening a guy's abdomen. Let me tell you one thing... that scene didn't sit well with me! Heck, I used to watch the TV show Bones, and it would cause me to be queasy at times. Now, I think the problem of tackling whether video games cause desensitization is a little bit harder than that, but it comes down to whether people still react to instances of real world violence. Although, I do want to note that it is important to keep in mind that people don't always react to shocking situations in the same way.