Aesthetics beat graphics as well. Some games have superb graphics but they just fill lifeless scenes. Here is a list that I made a while back:
Functionality, must be playable
Engaging, you must want to play it
Usable, you must be able to use it (here goes basic graphics that elevate it beyond Ascii, interface too)
Atmosphere, basic sound+aesthetic style+some lighting
Random or Replayable, a bit of all, but some games you play for ages while others are fire and forget, very hard to say what is and what isn't replayable, I don't find Dragon Age replayable yet I've played diablo 2 for over 400 hours
Simple or easy to learn, you can understand it quickly, you can pick it up and grasp what to do, several games people say are great I won't play because they start a jumbled mess
Deep and Complex, there is a lot more to learn
Dramatic/Cinematic, the bang from the explosions and the sound of all that happens, atmospheric but pointless
Visual eye candy, graphics go below sound and atmosphere