How are you not a gamer? If you buy games, and play them, you play games. That makes you a gamer. The whole "gamer" label is not a term used to describe fanbois, sad basement dwellers or the like.
Do you listen to music? Do you watch movies? Do you watch television? Do you browse the Internet? Entertainment. And so is gaming. For some reason we just feel the need to label the later. It's almost racism.:)
I think you are, in large, right. One stumbling block tho: when those kids grow up, they become insane parents themselves. And insane parents, as proven by several generations since the 70'ies, will forget ideals, become even more over-protecting and borderline insane - all for their children.:)