Why Kirsan Ilyumzhinov is so popular in the chess world? Kirsan Ilyumzhinov has just been re-elected as the next FIDE president again. He's so far beaten two World Chess Champions in the elections - Karpov and Kasparov, both by some absolutely big margins. 

What is his claim to (chess) fame?" What do people like about him to give him so much power? He's the real king in chess, the most powerful chess personnel in the world and dominating the chess scene.
I thought that Nigel Short summed it up pretty well here: http://www.chess.com/news/breaking-ilyumzhinov-beats-kasparov-110-61-at-fide-presidential-elections-4528

"There's nothing wrong with chess players. If you ask in the playing hall, I'll bet 9 out of 10 will vote for Kasparov. The problem is: delegates. If the delegate has received an incentive to vote in a particular way, it doesn't matter whatever reason or logic is presented to him."

Basically, many delegates voting for Ilyumzhinov received some strong form of compensation to do so. He consistently wins because he has money (much of which he gained while ruling Kalmykia) and has zero moral compunctions about how he uses it.