Loved this. I know these are not strictly song components, so they probably don't fit this particular video, but I think they are things that make Prince uniquely 'Princely'.
1) The sheer range of his ability to cross genres means that there are plenty of songs for every mood, for every life event. Whatever it is there's always a song that seems to fit.
2) I'd also say his ability to elevate his songs, that many saw as great already, to new heights when he played them live never fails to capture even the most 'fringe' fan and pull them into his world. The way he made subtle changes, or sometimes sweeping changes, to his songs when he played them live really did make his genius stand apart.