As for chess not being a sport, I think it is so Vladmir Kramnik, Gary Kasparov, Anatoly Karpov and Bobby Fischer are the greatest chess players up to now
Chess is a great game, but it's not a sport in my book.
If you are talking great chess players, you've missed out arguably the greatest - Capablanca.
Its tough to compare Capablanca, Morphy, Botvinnik, Alekhine etc because of the differences in time and understanding in theory on the game. But from the games I've seen Capablanca is up there. I think Kasparov and Karpov would beat him slightly more than he would them though but thats just an opinion after seeing more games.