I think it’s less “good jazz,” and more ‘jazz that fits the mood.’
I don’t want to listen to thrasher metal when I’m sitting in an italian restaurant, introducing my date to the family, and I don’t want to listen to jazz when it’s inappropriate.* I remember reading the blog of the Doom soundtrack, and he talked about the difficulty in creating soundtracks because you have to take music that was meshed to visual, auditory, and psychological happenings and create ‘just’ a piece. Going the other way, how difficult must it be to take musical compositions and match them well to gameplay… it blows my mind that there are people out there who do it so well, because there are definitely games that I loved because it was just a perfect combo, and others where they were saved from mediocrity with the addition of the right sound.
*Aside, I was trying to think an example of when jazz in a game was inappropriate, and couldn’t. Take from that what you will.