Can I say this kind of person is a sporty genius?
A sporty genius would be a genius who is sporty - Alan Turing was a mathematical genius and also a long-distance runner. He could be called a sporty genius.
Better could be a "sporting genius", it suggests someone who is clever at playing - "He is not the fastest player, but he reads the game better than anyone - a true sporting genius."
You might use "virtuoso" (more often used for musicians), "prodigy" (early developer) or "master"(also suggests seniority), or slightly more casually "wizard", but with "sporting" not "sporty".
A sporty genius is not idiomatic, at least not in the sense you intend. "sporty" doesn't refer to athleticism but to style, and "genius" is not usually used in the context of athletic ability, except perhaps to describe an athlete's play-making ability, where strategy is involved and the player has to see opportunities. That said, a genius at sports would be probably be understood to mean that the person is a very talented athlete and can play a number of sports well, or possibly any sport whatsoever because of their prodigious natural ability, just as a genius at baking would probably be understood to mean that the person can make a wide variety of delicious baked goods and perhaps understands all there is to know about flours and altitude and humidity and temperature and how they combine to affect the finished product.