So one way we can identify a game that is better than the rest is by saying that it is fun even when a player is losing. This appears to be more of a challenge. Something that is more of a challenge, of course, is more of an accomplishment when it is achieved.
This leads to two conclusions: one, to judge a game is this way, the game must end. Two, to judge a game in this way, the game must be capable of being lost. If a game never ends, we never find out who loses, so we'll never know if that person had fun losing or not. We're in the same position if the game does end, but guarantees that the player wins. As we pointed out above, anyone can make a game that is fun as long as the player wins.
A note about "fun": fun is not a good word, especially when applied to games. Fun could mean "diversion," but a bolt of lightning or a death in the family can be a diversion and not be considered fun. Fun could be considered a form of happiness, but happiness is itself a rather vague term (see this video from TED, recently posted on Darren Brown's blog). As I used the word fun above, I meant it in sense of being "engaging" or "interesting"--something we choose to participate as opposed to something we feel forced to participate in.
Back on track, this line of thinking leads to the "ultimate goal" I mentioned in The definition of a game. An ultimate goal ends the game when a player achieves it, and designates that player a "winner." It also suggests an "ultimate obstacle," something that also ends the game, but designates the player a "loser." Examples of ultimate obstacles include an opponent achieving the ultimate goal, running out of cards in traditional Solitaire, or running out of money in poker.
Just like some of the best movies don't have "happy endings," some of the most "fun" you can get out of great games is losing. If a game is great, then there should be a little win with each loss and a little loss with each win--in other words, there should be a drive to win quicker or more definitively next round, and there should be a recognition that this loss was closer to a win than the last loss. The true sense of progress comes not from the game's own progression (as defined as one of the components of a game), but from the players' continual mastering of the game and its strategies.
This is also why I think the best games are fairly short, including video games. To truly understand a game's nuances, the game must be played again and again to experiment with different strategies, and a long game makes that proposition very unappealing. Of course, multiplayer first-person shooters like Modern Warfare 2 usually have rounds that are around ten minutes long and are very easy to play over and over again. Board games usually last 45 minutes to an hour. Freecell usually takes me anywhere from five to ten minutes to get through. But because of their replay value--because the game is built to be played over and over again, these games wind up providing far more than the 80 hours that some of our more long-winded RPG's claim to provide, and they do so over the course of a lifetime instead of a cramming session over a long weekend.
A game that is played 80 hours over the course of ten minute games is almost guaranteed to have more of an impact on a player's life, because the player could have stopped playing after any one of those ten minute games. The games, after all, were complete--there was no plot twist waiting to happen or new weapon to discover. The only thing pulling the player back was the determination to beat the game better, more efficiently, and with more grace, and the only way to do that is to understand the deep nuances of the game--to understand its rules as completely as the one who created them...if not better.