Thomas' argument about how even in speech matters the parent is still the intermediary, I can say what I want, but the parent has control over what their children can here.
This was an interesting argument, but it kind of fell apart when I thought about the situation at hand.
Essentially: How can a child be at a game store, in position to buy a game, without the parent having relinquished (or be ineffective at) their roll as the intermediary?
If the parents want a store to drop their child off at confident that they will not be sold a violent game, it is a failing of the market to create such a store. Such stores could exist side by side with stores that do sell violent games to children (the situation we currently have). It is not the place of government to create that type of store at the cost of every store that would not follow the model.
Furthermore, legislation against the child buying that M-rated game isn't going to do anything to stop all the other forms of speech the child will potentially be subject to while in the store without supervision or on the way to/from the store.
As Scaila says in his opinion, such legislation does not enforce parental authority, but instead imposes government authority.