If you learned that the article was in error, and the concept was actually introduced by some respectable source, would that change your opinion of it?

That's a completely irrelevant hypothetical, because the "apex fallacy" (which I shall continue to put in quotes due to the fact that it's not an actual fallacy) is a rhetorical argument set against data driven conclusions. It is literal nonsense. I'm racking my brain, and the only good analogy I can come up with is if I said, "Man Texas is hot." And you replied, "NO, that's the 'apex fallacy'. Only its really hot days are hot, and sometimes it's hotter in Minnesota." If you can find a better one, I'd like to hear it. Or, if there were some actual scholarship on the matter, then yes, I would take it a lot more seriously, even if I disagreed I wouldn't dismiss it out of hand. Fortunately, we don't have to resort to that here.

I'm not sure I get the sports analogy, unless we're relating one's business and administrative acumen to their physicality. On the subject of chess, it might just be a numbers game. That's what Yasser Seirawan suggests in this book, although it is speculation. He estimates the numbers of males and females who play chess and based on the huge number of men compared to women who play, estimates that the odds are against women for having a world class player (if we assume random chance). I'm not going to defend or rebuke that claim, because I have no idea; just putting it out there, because it's the only thing I've ever read about it. The same can't be said of women in the business world, because they occupy a proportionate number of low and middle jobs, but lack representation at the top.