The real question is, what can't we learn from games? There is no subject, no matter how complex that cannot be taught with engaging game mechanics. Angry Birds and Crush the Castle teach us rudimentary physics, and it is not hard to see how more complex physics could be taught with similar mechanics. Even the disgusting or taboo could be taught through game mechanics. I hate the idea of the power of games being abused in such a mannor, but i can easily see how a game teaching such horrendous things as rape and torture can be made to be enjoyable, even subversive, slowly training your responses so that what would originally be repulsive is seen as a reward.
On a lighter note, there's so much good that can be taught though games. Mathematics can be taught subtly through puzzle mechanics without it becoming an obvious educational game. History can be taught through games that reward us for exploring historically accurate environments. Military tactics can be taught through RTS and FPS action games. There is no subject that games cannot make enjoyable and informative. What it really comes down to is what should be taught, why, and how. It is easy in games to subversively indoctrinate people, both deliberately and accidentally. Extra credits did an episode on it that can be found here. If you don't know them and you're at all interested, check out all their episodes, it's good stuff.
What's more interesting than the things games are able to teach us, are the things games allow us to explore and learn more about ourselves from. Games allow us to explore possible realities where certain points of view are held strong, or certain events occurred that create societies that are vastly different from the current world. They allow us to explore points of view taken to the absolute extreme, or the nature of humanity under extreme adversity. They also allow us to explore the very meaning of humanity itself. What makes a human a person? What separates us from animals? Or robots? Even bad games can teach us powerful things about humanity. Games where the characters fall into the uncanny valley (another thing Extra Credits have done an episode on), where they just don't feel like real people, where something is just off, they allow us to explore essential traits of real people that we would never have noticed were present, but are disturbing in their absence.
There's also a lot games can teach us about ourselves as a person. How you choose to play an open ended game can teach you a lot about both who you are, and who you want to be. For example, there are only ever two roles i really enjoy playing in any team based strategy game, regardless of the game and gameplay. I'm always either a tank, or a defender. I enjoy roles that force me to work as a team with the people around me. Neither role is really able to function solo, they rely on support from others, or provide that support. I don't like to be the damage dealer, or the solo'er. So basically I'm a team player, and i don't like being the center of attention. I'll happily take a death on my K/D ratio if it means my team get an advantage over the other. And I'm happiest whenmy job makes the job of my teammates easier.