I think that videogames teach something about ourselves once you dip into the multiplayer arena - especially when you have more than 2 players. This puts you in a position of forming alliances (temporary or otherwise) and seeing how you behave in those circumstances can be interesting...

Playing Worms Armageddon may seem initially a simple fun experience, but spend any time on it and the turn-based nature, twinned with a multiplayer experience (which will differ again between PC/LAN/Web and console 1 screen) and you see that the game has many hidden depths.

Even stuff like Mario Party makes you think - who do I steal coins or stars from in a 4 player game for instance?

Even 2 player games like Joust offer bonuses for temporarily forming alliances in some levels , and Balloon Flight for the NES has a similar mechanic in its bonus levels.

Single player games can only move toward making one learn something about oneself when your actions set up non pre-scripted consequences and each player's experience is unique because of that.