I think right off the bat, we'd have hundreds if not thousands of lawsuits flying. Most game companies would simply cease to exist.. remember, Sega and Nintendo even had a gun!
The next steps would be interesting.. would they want registration of our games? Would there be "buy back" programs? Unlike a physical object, I can go ahead and give you my dvd or cd, but is the game really gone?
And that's not even considering the backlash. Many of us - like myself - grew up with video games. (Kid Icarus ftw!) And now many of us are technology professionals with massive platforms, discretionary funds, and near legendary stubbornness.
I think it would make the SOPA reaction look like a fart in the wind.
Lest we go into how the pros/cons of said bannable things - one could argue that shit food is the only option of the poor, and cars allow people to travel, but then, games are another piece of the puzzle that distract people enough that they don't need to think about the fucking delusion they buy into.
It's hard to deal with hypotheticals like this because you haven't been very specific about the nature or degree of the (hypothetical) causal link. It's not beyond the bounds of possibility that the repetitive and constrained context of video games were a risk factor, as opposed to the depiction of gore - so that Pacman or Space Invaders could indeed have an impact on the small number of vulnerable minds, in similar fashion to the small but real possibility that video games can trigger epileptic seizures in some people.
ultimately, guns are the only things which can shoot.
I think everyone would agree that certain types of content should not be available until you have reached a certain level of maturity.
For the government to do that would entail amending the constitution, since SCOTUS has already ruled that doing so violates the First Amendment.
You find that a difficult question to answer?