What the case came down to was whether violence can be treated the same way as sex. Ginsberg v. NY, a case from the 60s, gave an exception to the normal obscenity test--media could be regulated if it depicted sex and was sold to minors. Ginsberg v. NY, however, didn't touch on violence, and the issue was whether Ginsberg v. NY is content-specific, and only limited to sex, or whether the fact that that decision hinges upon harm done to youth means that other media that harm youth, ie, through exposure to violence, can be included in the exception. And, as you guys may guess, the trouble comes from the fact that damage can't really be shown.
That being said, if it was ruled Constitutional, I wouldn't have a problem with this law. Community values should reinforce parental values. There is a reach to what parents can do and control, everyone knows that.