The irony of being a prodigy is that it is indeed a facade, because it's not that the achievements are new, just that the achiever is.
This is why it feels empty. Because although you did something a few years earlier than other people, lots and lots of other people already did it, are doing it, and will be doing it soon.
The rat race is one of relative achievement. One can pile on all the plaudits and laurels in the world and it still comes down to jumping through other people's hoops for approval.
The only thing that doesn't feel fake is absolute achievement -- when you do something new, regardless of age, and regardless of media coverage or getting puppy snacks from the outstretched palms of condescending adults.
I think it's ten orders of magnitude easier to say "do something new," than it is to actually do something new. It's tempting to believe that prodigies burn themselves out because they get cynical about the "rat race", but many burn themselves out by trying to revolutionize the world at a young age, without realizing that the world is a damned hard place to revolutionize. (You can see this phenomenon in the kid in the cited article -- he's ten, and already convinced that he's going to revolutionize a branch of astrophysics. That's a dangerous kind of immodesty.)
Obviously, it's good to strive for creativity and novelty in your work, but you also have to maintain a sense of perspective: if you've set your goals so high that your definition of "achievement" is isomorphic to "originality", then you're probably in for a lifetime of disappointment. It's a hard problem to be original -- there are a lot of other people in the world, and most of them are trying to be original, too. In fact, being original is a lot like being famous, because you can strive for it, but your success is largely determined by what other people do; it's probably bad to condition your self-esteem on the actions of other people.
For what it's worth, here's my half-formed philosophy: you have to do whatever it is that gives you a sense of personal satisfaction and contentment. Your accomplishments don't have to be great; they don't have to be original; they don't have to make you famous. As long as you can look in the mirror in the morning and feel excitement about the day, you're doing pretty well.
Perhaps I should have described another trap. It is too easy to grow up with the sense that one should work on only grand things.
"The worthwhile problems are the ones you can really solve or help solve, the ones you can really contribute something to. [...] No problem is too small or too trivial if we can really do something about it."