He stole the guns. That's the point. He didn't buy those guns, he stole them. If he would have tried to buy them, he would not have been able to. Current regulations already in place would have prevented him from purchasing any of them.
If his mom, a legal and responsible American, would have been prevented from buying them, then he would have either stole whatever guns she had or stole someone else's guns. The fact that he had an assault rifle didn't matter in this case.
If you're shooting a bunch of little kids, a shotgun, pistol, rifle, assault rifle, doesn't matter, any of them are going to do the job.
If the guy would have got into a shootout with a bystander who was trying to help, and he used an assault rifle that he legally purchased to out gun the potential hero, that would be something to consider. But if he's executing a bunch of unarmed little kids with a gun that he stole, then putting additional regulations on legal purchasers of that type of gun is not going to help.