It does not stop there. As Medea's example shows, games can get you interested in all kinds of stuff you would not have looked up without the initiative.Ok only game that can teach you something, besides thinking games, is Age of Mythology, since it has the full Mythology info on every unit, god and so on.
Probably mentioned before, but the best examples lately would be Civilization and Fate Of The World.
The first gives you a glimpse of all the cool stuff makind came up with throughout the ages, while the second makes you scour wikipedia for background info on very current issues, because you want to know what it means when you make decisions like "Advocate Biochar".
I found it cute when James from EC talked about his life in one episode, and said "I've been to almost every Civ wonder that is still standing". Every gamer could immediately relate to that. And the amount of people who grew up with computers as a normal part of their lives is growing all the time.
And the world is slowly realizing this. Also thanks to developments "true" gamers tend to frown upon, like casual or family games, your "usual reaction" is becoming less and less popular.
Then suddenly it is not a sign of coolness anymore if you have never even heard of WoW, whether you care about it or not. Or a sign of virtue if you are among those politicians who reject the internet and still make their secretary print out their emails.
People who like to confuse cause and effect when kids who fantasize about shooting their teachers also play similar games... probably do this because people still alienated by the subject tend to believe them. It is, after all, an easy scapegoat for all kinds of problems.
But their numbers are dwindling. So just hang in there.