Don't get too fixated on the singular adjective "classic" -- I needed to call this list something, and that seemed like the best descriptor to quickly convey what I was going for. Read the story in the OP and ask yourself what kind of games do you think that kid should be aware of, or are you disappointed that he probably doesn't know? What games do you think every gamer should at least witness before they die? What games are venerable oldies that helped shaped the gaming industry? So long as you aren't specifically picking games because they're your favorites, make of the list what you will, and understand that others will be doing the same.
My personal thoughts -- and these are strictly personal thoughts -- are that the list should greatly emphasize older games, but I don't have some magical cut-off for when games stop being older and start being middle-aged or newer. Thus, I didn't want to explicitly define any restrictions. I'm sorry if that muddies the waters.