Videogames can be banned despite freedom of speech. Comics were banned way back when to follow certain guidelines, (Remember the comic code?
How does this happen? Well, they thing is, these people don't consider videogames art, and may not even consider them expression; they think of videogames are merely entertainment, or a toy. Yes; it's false but this is how people who seek to ban videogames think.
If they didn't, they'd be banning books.
Some videogames do have a violent influence.. many things have violent influences... many things have positive influences; but this isn't the point! People play video-games under their own will and accept to commit violent actions under their own will, the whole issue falls under a greater problem: There is no personal accountability in the world, we blame culture, the media, religion, mental illness, but never the individual. It's a state of affairs that won't go away unless there's a lot of changes in the ways people think.