I think a genius is someone who plays what sounds like a new solution to a problem, a fresh, new approach, that is instantly recognizable as "the next step forward." It is truly bound up in the person - it is not "inevitable," and perhaps would not exist if that person had not come along. Thelonious Monk is a good example - he put forward a new approach that others could use in their own playing. Coltrane, too, in the way he led the power approach to playing.
Some caveats:
Genius is not eternal. It erupts, maintains for a few years, then declines.
Genius has to be useful and enjoyable. Many people are labeled geniuses who are just annoying. On the classical side, Harry Partch comes to mind. On a parallel note, mental illness should not be confused with genius.
Some jazz musicians/composers/arrangers who I would consider geniuses: Lester Young, Fletcher Henderson, Louis Armstrong, Charlie Parker, Bud Powell, Jimmy Smith.