I think the thing that stuck with me most after reading Jesse Schell's book was when he defined play as stuff you do because you want to do it, not because you're obligated to. Although it sounds tautological, I think there's something profound there. I think we're wired such that as soon as we feel obliged to do something, fun is killed.
I notice this over and over again when I'm playing games. "I should play this because it got a high score on gamerankings and I should try to figure out why everyone loves it so much." "I should play this because my friend made it and I owe it to him." "I should play this because I spent $60 to buy it and if I don't play it that money will be wasted." When I'm in one of these moods, the littlest frustration becomes insurmountable and eventually just putting the disk in the console seems a herculean task.
This is something I've known for a while as a manager. It depends on the person, but if you ask somebody to do something, they often put on their defensive hat and start explaining why it isn't going to work. (Particularly if they're not getting paid.) But if you ask them, "Hey, what do you want to work on next?" they almost always will pick something that needs to be done and then they're having fun doing it and doing what they want to do. This is the "make them feel like it's their idea" trick, but I don't believe it's disingenuous - it really is their idea. Sometimes it's an idea you didn't even think of.
How might it influence game design? It argues that the cheaper we can make our games, the better. Free to play, costs money to buff/upgrade/whatever, looks even better. "I'm playing because I want to, not because I plunked down $x on the membership and feel obligated." (Right now, the $20 I plunked down on Galactrix is putting me in the 'I'm obligated to play this more zone' and I am starting to build up resentment. I am getting a lot of play out of it, though, and am starting to get colored hexagans permanently burned on my retinas...)
RPG's, with their lists of tasks you have to accomplish to get to the next...task...can easily push you over from "I'm having fun" to "I'm doing a chore." Simply putting up that "percentage complete" number can make those optional fun sidetasks you put in your game into obligations; there was a lot of grousing on the forums about how Spider-Man 2 forced people into mindless repetition if they wanted to 100% it. We never really intended for people to 100% it, and were boggled that people would try if they weren't having fun doing it, but there they were. The most fun I have when playing Spidey 2 is aimlessly swinging around Manhattan...no obligations at all...
Going back to Galactrix, they have a multiplayer mode where the further you get in single-player the better you'll be at multiplayer. You're obligated to play single-player to play multi-player. (There's no multiplayer community critical mass that I can tell - Schizoid has the same problem - I'll talk about that in another post.) Same goes for Peggle XBLA - single-player unlocks the characters you use in multiplayer. One game that stands out as being different is Spectromancer - with Spectromancer, if PvP is your thing, multiplayer acts as if you have a full deck to pull from. You're not obligated to play single-player, and thus single-player is less of a chore, something worth playing in its own right.