The only problem? There’s no data to support that position. There is evidence that limiting access to guns can help limit violence wrought by those machines. In particular, there’s evidence to show that the Assault Weapons Ban helped to limit gun violence on the Mexican-American border. And in states where gun ownership is high and gun laws are lax, violence rates are higher.
On the other hand, there’s absolutely no conclusive evidence showing that video games are the root cause of violence. There are countries with much lower rates of violence that have much higher consumption of video games.