Actually... gun safety should be taught at a young age... I started teaching my daughter when she was 4, and bought her a .25 pistol that she could properly hold and chamber a round by herself (two very basic requirements before you start teaching a child how to handle a weapon). She is over 21 now and has attained marksman awards in the military, and is currently overseas.
Now whether this "NRA game" actually does this, is another issue. There is no substitute for supervised sessions at the range.
That's like anything else, though... one can't expect video games to do their parenting for them.
As for the unfortunate shooting... the mother was going to commit the son. Crazy people will get weapons no matter how much "control" there is. The difference is we live in liquid brain matter of mass media through 24/7 cable news and the Internet... so just about any shooting is more in your face.