In practice there are many games without scoring systems, without a method of determining victory. However in the practice of table top gaming I do not consider them games. Instead, they are activities. Games specifically contain the concept of (competitive) victory determination and other things don't. This is a recursive definition. Games are those things with scoring systems. Scoring systems define those things which are games. That recursion is unfortunately unavoidable and perhaps even axiomatic.
Fun, while desirable, has no function in the definition of what is and isn't a game. Sure, things are better when they're fun (for whatever your local definition of "fun" is), but there's nothing in the logical definition of what is and is not a game which requires considering "fun".
Scoring can be anything. Who crosses this line first? Who gets the largest number of X, smallest number of Y? Who is not eliminated? Who gets the Frobbox? Whatever the method, it determines victory. Most money, checkmate, first over the line, last one standing, most points, player with the Snitch, least points -- they're all scoring methods as they set the criteria for victory and thus the entire focus and goal of the game.
There's a built in assumption there, that games are played for victory. But like the differentiation of games versus activities, it isn't so automatic. Many players don't play to win. They have various other reasons and motivations: they want to see what happens, they're along for the ride, something to fiddle with while socialising, make sure that John doesn't win, whatever. In some cases with such player's there's even a counter-morality that trying to win (too hard) is wrong or at least socially unwelcome. However in line with the above differentiation between games and activities as goal-centric activities (ie scoring), such players are not actually playing the game. They have not accepted the definitional cornerstone of the game definition, that victory per XYZ is the purpose of the game (for whatever XYZ scoring method that game has). They're engaged in an activity which masquerades as a game. Presumably at some point the system will pop up and annoints a "winner" in order to end the shared social activity, but the players never accepted that scoring goal for themselves and thus are not striving for victory per that goal. To that extent they are not playing a game, they're involved in a social activity, just one with game-like trappings.
A: No. Scoring is relevant, even in inelegant games. There are many games that are not elegant that still need scoring systems. In fact, there are many games that are not elegant that I would not bother playing if they did not have a scoring system. Contrariwise, there are some very elegant (or just outright fun) games that I'd be willing to play, even if they didn't have a scoring system.
Q: Is scoring generally important, regardless of your aesthetic goal as a game designer?
A: Hmmmnnn... That's a tough question. A lot of this depends on what counts as a scoring system. Two of my favorite Invisible City games are Fact Party ( http://www.invisible-city.com/play/55/fact-party ) and Jam Doodle ( http://www.invisible-city.com/play/92/jam-doodle ). Fact Party explicitly states that there are no winners or losers. Jam Doodle's win/loss conditions are deliberately vague. A co-operative game of mine that's been licensed for publication (probably late '09!) doesn't have a "score" per se, but has very clear win/loss conditions. Does every game with a win/loss condition have a scoring system by definition?
I think that we, and the game-playing masses, are used to games that have definite end-points and have a clear winner. I think that people in general are used to the story structure of beginning-middle-end, and media (books, movies, games) that doesn't follow that format violates an implicit social contract; it's harder for people to understand, relate to, and accept. In that respect, I think a scoring system is important for a game to have.
Is it essential? Can we make games that don't have a scoring system? Will they be fun to play? I think that the answer to all three is a resounding, "Yes!"
Class is starting... Have to go now!
I love your answer. Thanks! THe way you restate my question is a little different than the question asked. You quote "Is scoring generally important, regardless of your aesthetic goal as a game designer?" I meant: Is scoring the most important aspect in game design in general, or is it only the most important thing in elegant design? I think your answer is sufficiant anyway so it doesn't really matter. But I did want to clearify.