I guess it depends what the threshold for "genius" is. Obviously Carmack and Gates are very bright people who've accomplished a lot, but let's be honest, they're not exactly at the level of DaVinci or Einstein, or even Feynman.
And I do think it's ego problem if somebody goes around defining themselves as a genius. One of the things I'm always struck by is the fact that many of the smartest people I know are incredibly humble. They're smart enough to realize all the things they don't know.
Feynman was perversely proud of the fact that when tested (as a child?), he _didn't_ have a "genius" IQ. Wikipedia claims it was 125, but I thought I'd heard him claim it was 134, one point too low to qualify for Mensa. That's just my memory of a brief anecdote he told a group of undergrads over 30 years ago, so I likely have the details wrong.
He claimed that any genius could win a Nobel prize, but that he'd done really well to have won one as a non-genius!
I've never believed Feynman's self-reported IQ. Reading his breezy autobiographical books, he had a habit of somehow bragging by underplaying his abilities, making his accomplishments miraculous/lucky/etc. I suspect the IQ legend is just a part of that.
And I do think it's ego problem if somebody goes around defining themselves as a genius. One of the things I'm always struck by is the fact that many of the smartest people I know are incredibly humble. They're smart enough to realize all the things they don't know.