I obviously interpreted the article very differently than you did. I don't see the fact that you've never played sports before as a disadvantage in such a hypothetical screening process at all. You say that you have a mild coordination problem, but again I don't see that as a disadvantage. The definition of "sport" is very loosely applied these days. Even poker is considered by many people a "sport" these days (at least in North America). So replace ultimate frisbee with poker and your coordination argument is no longer meaningful. I've played sports with many people who have physical disabilities ranging from muscular dystrophy, cerebral palsy, to blindness or deafness and in every case I've seen it's very easy to separate those who are willing to put in effort, willing to try something new, willing to take risks, and show sportsmanship from those who aren't.
I believe what the author is advocating is the use of a sport (I'll call it a competitive game to be more accurate) to screen for the ability to persevere in the face of adversity, show drive, and most importantly show willingness to learn in an unfamiliar, unexpected situation. I could easily make an argument for why each of those traits are desirable to have in an employee.
> But you would never consider hiring me so you'll never see that
I think the author would choose not to hire you, not based on your lack of coordination or inexperience in sports, but would do so based on your stubbornness and unwilliginess to participate in something new. I equate this to the same attitude that I occasionally see in programmers who dismiss new technologies without even giving them a fair chance.
That said I can see how it would be possible to misinterpret the author's use of the word "sport" for a physically competitive game - and if that's the case then what I said above doesn't apply. Nonetheless, in my opinion even if the author had strictly meant a "sport" in terms of a physically competitive game there are some valid points that can be taken from the article.