Is it government's responsibility to determine the causes of our actions, and to stop us from harming ourselves? Or, is it government's responsibility merely to create an environment wherein our actual actions, as they directly affect others, have consequences?
The former notion has created something of a slippery slope of late, as expected. It started with drugs (excluding alcohol, of course), more recently including cigarettes. Then, it was extended to opinions, in the case of "hate" crimes. Next was unhealthy foods, like the banning of trans fats. Now, it's being extended to video games.
As individuals, we're legally responsible for the results of our actions. Hating a racial group shouldn't be against the law; killing someone, regardless of their race, should be. A crime isn't made worse by virtue of one's racism, and it isn't made better if one loves the victim's race. And, killing someone because of the race isn't excused by one's racism, which is an implicit assumption behind hate crimes--that one is somehow compelled to commit a crime by virtue of one's racism.
The same with video games--even if they cause some people to commit a crime, that's not the same as committing the crime itself. And whether or not they're bad for children is for each child's parents to decide.