Indeed. Such a game would be nigh-impossible to find. An urban legend, striking fear into the hearts of superstitious, cowardly art critics...wait, what's this?!
BAM.
The Legend of Zelda: Majora's Mask answers everything you've put forth so far. If you haven't played the game, shame on you. Go do that right now. Also, this will make more sense if you have.
The game has two main "rules", as you call them: the repetition of the three day cycle, and the masks that change your abilities in-game.
Now, you can dismiss these two things as simply elements of a game design that's meant to be different from the mega-success of Ocarina of Time, but where's the fun in that? Let's look at both rules, and see what they have to contribute to the artistry of the game as a whole:
The time limit. You only have three in-game days to save the world. And you can't. For a long time, you have to retreat at the end of each cycle, because you're powerless to stop the moon from falling. You fail, again and again, before you're finally able to succeed. That alone would be a decent theme, but the game goes further. Except for masks and a few other items, every time you start over, you start from scratch. You're back to square one every time you save (barring the statues, but those are only good for one use and not really relevant to the point). The point is, a central mechanic of the game is designed to make the player feel helpless against an omnipresent threat, until eventually you're strong enough to take it on.
[Incidentally, I've never sat through the game to see the destruction of the town. I couldn't stand it.]
The masks. The masks, again, alter gameplay somewhat, but why masks? Why not talismans, or tunics like in OoT? Masks have a strong anthropological significance. Tribes all over the world use masks in their rituals, and to this day masks are used in theatre performances. More importantly, though, the game offers commentary on the masks everyone wears, in day to day life. Anju, the innkeeper, has a mask of someone who is there to serve you with a smile, but the most involved sidequest in the game reveals how much is going on beneath the surface. Link wears masks to interact with the townspeople, just as you wear a mask to interact with your townspeople. Anytime you've felt miserable but elected to put on a happy face, you've worn a mask, and, indirectly, helped me prove objectively that Majora's Mask is awesome.
I could go on about the things that make this game a great work of art, but I won't right now, as it's three thirty in the morning, and I am sleepy.
If nothing else, the amount of academic waffling produced by games (see: above) should convince people that it's an artform in the making.
