People who perform these acts did NOT get the idea from some video game or thing they saw in a movie or television. If someone goes on a no-joke gun rampage in their school or workplace for no discernible reason, it is because these people were mentally unstable and would have been set off by anything.
Now, to answer the question of your topic, violence is allowed because of the terms of free-speech, in that no content can be banned from merely existing, unless it is the photographic depiction of something like child pornography.
But why is there violence in movies and video games? Because in the broad sense, we've already made up our minds on violence. We LIKE it. We like guns, we like swords, we like fatalities, we like zombies; WE LIKE VIOLENCE. When it's simulated, of course.
But yeah, the answer to the question of "Did playing "Doom" make these kids do this...?" is no. Any reasonable human being thinking clearly and acting honestly can see that. You want a statistic?
ZERO
That's the exact number of studies, experiments and pieces of evidence- in EXISTENCE - that even come CLOSE to even STARTING to prove a link between violent games and real-world violence. There is more concrete worthwhile evidence for the existences of Bigfoot, the Loch Ness Monster, Iraqi WMDs and God COMBINED, than there is to THIS moronic claim.
And y'know what? It doesn't matter. Not to the people propping it up. Not one bit. Know why? Because they BELIEVE it.
On every side, of every facet of every issue known, unknown, or ever known to the history of mankind, there have always been two kinds of people:
Thinkers, and Believers.
The folks who genuinely posit that violent video games, or movies, or music or TV , or books, or paintings, or whatever else directly cause real-world violence are BELIEVERS. They HAVE to be. See, you can BELIEVE anything you want, but for something to be a thought, it has to make sense. It has to be based in some concrete conception of fact or reason. And this? This doesn't pass that test. This isn't worthy of being called a thought. It's merely a belief, and that means you're not going to change the minds of the people holding it. They're either dumb enough to believe it, crazy enough that it actually makes SENSE to them, or they're being disingenuous for a broader agenda. Get that?
STUPID...
INSANE...
or LYING...
So, uh, yeah. Hate to bring you the bad news, but there it is. Nothing you can say, nothing I can say, nothing anyone can say will make the pro-gaming-censorship douchebags come to their senses. They're BELIEVERS.