I can't speak for the painting side of things, but no, not everyone can learn how to play a piano. For one thing, left-hand / right-hand independence isn't a universal trait, and isn't something that can always be "learned" (there's a reason why chord / melody books are so popular). Finger independence is even trickier. Sight reading, relative (or even perfect) pitch -- these are _talents_ that make a good performance possible that often can't be learned by those who lack the talent.
Designing algorithms, debugging, interfacing with hardware, finding efficiency -- the myriad of things that go with programming, these things can be done by a layperson the same way a wealthy hobbyist pianist can plunk out "Music Box Dancer" on their $10,000 grand piano -- but will they be done well? Will the hobbyist pianist give a great performance? They might be happy with it, and that's fine. But will they get to Carnegie Hall? No?
I'm not saying the hobbyist pianist shouldn't try any more than I'd say anyone who wants to write a program shouldn't try -- but the article suggests there's no real benefit to "talent" and that's just silly. There _are_ rockstar programmers, and we should acknowledge them, just as there are great concert pianists. And everyone should be encouraged to try both piano and programming. But not everyone will be successful at either or both of them.