Which skill specifically is the one that some students have, and other students cannot be taught?

There is no particular, identifiable, atomic skill that they're calling "programming skills". Like any other performance or talent, it is made up of a jillion jillion component skills. And I don't see them claiming that any particular skill cannot be taught, only that it is less likely to be taught to some than others with a given amount of instruction.

They take the grade in class as a proxy for general programming skills. That has it's own issues, but I'd expect it to have decent merit on population statistics.

I don't see any "magic" coming out of further reduction, here.

"Our teaching style of programming has a 'double hump'." instead?)

Because they claim the empirical observation that the double hump is prevalent across the distribution of classes, not just in any particular class. Yes, maybe with a different teaching method, the bottom cluster could do better. Maybe I would have been a better basketball player than Kobe Bryan is someone had taught me differently as well. But they didn't. Oh well.

I recalled this story from years ago and tracked it down. Their main claim was that a particular test at the beginning of the course accurately predicted the outcome of the course in terms of their grade. Someone else mentioned that in the later papers, they say that their test is no longer predictive.