Is there any research on the effect of violent video games on people who are mentally ill?
Arguably there is far less justification to not giving a gun to someone who is mentally ill or not letting them join the military (present danger) than it is to denying them their first amendment rights (no present danger). Of course, I'd imagine if a mentally ill person excessively plays a specific game, there are already procedures for his psychiatrist to take action. A blanket ban is silly, though (what if game is therapeutic for them?)
Overall I'm not comfortable on a "war on the mentally ill" either. It's certainly wrong that Rikers Island is currently the biggest mental institution in the country, but we have to remember that they're more likely to be victims of violent crime than its perpetrators. If your goal is to decrease violence, then stigmatizing the mentally ill further than they already are and scaring them away from treatment (especially the people who need treatment the most), will actually increase violence and work against you.