I believe that red john is a genius that enjoys puzzles, because he has created a very intricated network of disciples which he really doesn't need (you might argue that his people in the FBI and CBI have helped him on several occasions, but apart from the killing of vasco's team, he would never have gotten in such situations if he didn't have disciples in the first place, and rebecca's "hiring" was a rather "momentary" thing) and it can therefore be argued that he has only created that network for the hell of it, so to speak. Because of that, I think Red John is the man at the puzzle store, in the episode of the universal hack and the dead mathematical genius, and that he respects Jane enough not to kill him beause jane beat him at chess.