I've never heard "the Aristocrats" joke, but it is a classic that many comedians tell with their own stylings. It's supposed to be extremely off-color. IT kind of demonstrates your comedic chops. There was a movie several years ago, maybe by one of Penn or Teller, that goes into different comedians telling it and the history of it. At any rate, IIRC from a description of the movie, there was some sort of public performance right after 9/11, one of the first, back when everyone couldn't figure out how to get going back to normality and resume with life. So, the movie picks up on how Gilbert Gottfried loosened everyone up by going up and doing his version of the joke.
In that spirit, I do agree losing him was tragic. I heard he was calling for help his last couple of days, but no one would come because his voice was so grating.