What's the mystery there? Bobby Fischer was completely obsessed with chess and played and studied it incessantly.
9 years of manic dedication and he "suddenly" got good.
His mother spoke something like 8 languages and his father was a Hungarian physicist who headed the Theoretical Mechanics section of the Naval Ordnance Laboratory and was an expert in elasticity and fluid dynamics.
One famous story about his memory:
"One day when he was in Iceland, Fischer called Frederick Olaffson, Iceland's only Grandmaster. Olaffson's Icelandic-speaking daughter answered the phone and explained her parents were out and would return at suppertime. Fischer understood nothing that was said because he did not know the language. But he listened, apologized and hung up. Later that day Fischer met with another Icelandic player who spoke English. He explained what had happened and repeated every Icelandic word he had heard on the phone, imitating the sounds with perfect inflection. The Icelandic player translated the message word for word for Fischer."
Despite being prodigiously "intelligent", it still took years of dedication to get good, and years more to get really good.
Plenty of average people undoubtedly beat him at chess when he was a kid. When you think about it, it should be obvious that he was always that smart. Just because you're a kid and don't know anything yet doesn't mean you aren't smart. "Smarts" is not the same as skill.
Incidentally, his record as the youngest grandmaster in history lasted for many years until it was broken by Judit Polgar, whose father was explicitly running an experiment with his daughters to prove that prodigies are made, not born. All three daughters became chess experts. He explained that Judit, the youngest, was the most successful because she worked the hardest. She's the only female ever ranked in the top-10 of the "Men's" ratings list.
Since then, many people have gone on to break the youngest-grandmaster record at younger and younger ages. I can only assume that if being a classical composer had as much of a "lobby" as chess (parents pushing their children into it, reward structures), we'd see more Mozarts as well.
The reason it takes HARD work is because even geniuses aren't that genius. If you look at the top level of any objectively measurable and well-subscribed field, there is generally less than a 1% difference between the best, whether it's sprinting, bike racing, weight lifting, or chess.
Knowledge builds on knowledge and skill builds on skill. If you think of it like compound interest, a few percent difference between two individuals at any given moment eventually turns into a huge dividend a decade or three later.
For chess, if you take two average players rated 1500 each, and one improves at 2% "interest" and the other at 4% "interest", in 10 years the former player will be rated in the 1800s (moving from class C to class A), and the latter will be rated in the 2200s (National Master).
To become a Grandmaster (typically 2500+) in 10 years, that's an "interest" rate of about 5.3%.
Meanwhile, a super-genius with a 7% compounding rate who puts in 7 years and then burns out will be stuck at ~2400, International Master level.
Humans occupy a pretty narrow raw talent niche. The best people tend to be pretty tightly clustered together. I'm not smarter than I was when I was young, but I have compounded YEARS of knowledge and experience to the point where I can vastly outperform my younger, smarter self.