Electroplankton probably fits that descrption as well. I don't own it (no DS), but apparently you just sort of fiddle about with various little fiddly things and somehow this produces simple melodies.
There are games that have tried to offer more than fun, or things other than fun.
Killer7 comes to mind -- it had fairly rote gameplay, but an enormously convoluted plot with some interesting things to say about, of all things, politics. [Added: Looks like Shannon Drake beat me to it.
]
Shadow of the Colossus was fun, but also filled me with awe at its beauty. It was also one of the first games to make me question the morality of my actions. Previously, morality was generally clear-cut in games, in my experience. You were either a "good guy," (e.g. Mario, out to save the princess) or a "bad guy" (e.g. the protagonist of any
Grand Theft Auto game).
Spoilers for SotC below:
In
SotC, I saw a protagonist who would do anything -- my theory was that he wished to bring back his lost love -- but for the first time I really questioned whether he
should. I didn't trust Dormin at all, and some of the death sequences of the colossi were so heart-wrenchingly beautiful that they made my guts physically
ache. Was the life of this one girl truly worth the lives of sixteen glorious colossi? Was she worth the effect on the protagonist? What if he died saving her?
The ending was remarkable, particularly since I'd played their previous game,
ICO. She lives, but at what price?
End spoilers.
Of course I thought
SotC also had great gameplay. It was fun. So it's an example where artistry doesn't conflict with fun and engaging gameplay. I think Scopique's second paragraph is apt -- gaming is an interactive medium. Make the interactivity too rote, too dull, without sufficient reward in terms of story, fun, and/or atmosphere, and you're left with little reason to play the game.