Short one today:
I think that game aesthetics ideally have the following properties (in order of importance):
1) Communicative -Clearly delineate and hopefully even explain mechanical distinctions (see Affordance)
2) Interesting -Some aspect about the visuals grabs the attention of viewers unfamiliar with the game
3) Unobtrusive -The visuals can be viewed for a long period of time without becoming irritating (Note that this can be achieved either through minimalism/abstraction or through lavish attention to detail/realism)