Video games should use jazz more. Not just for soundtracks, though that would be nice too. Jazz encompasses much more than sound. It's a flavor. It's also a ruleset. Or a philosophy.
The genius of one of the best things to come from America—yeah, really—is that the musical artform embodies a flexible set of colors, gestures and attitudes that you can apply to damn near anything in life. Poetry, literature, painting, movies… all of these disciplines absorbed and re-configured themselves around the jazz idiom, embracing the ethos of improvisation.
Too few video games follow that example—L.A. Noire does, but more in terms of mood than mechanics—but Beat Sneak Bandit shows the way.