The OED has long been my nemesis, so it does not surprise me that it would continue to fight and win. 😉
Seriously though, I didn't find that argument all that compelling other than the old "language evolves" point, which mostly means that people make grammar mistakes and eventually everyone accepts it and the rules change. But that doesn't change the fact that they were (in the past 300 years or so) generally agreed upon mistakes in their time. To go back to 1375 for an example of how "they" was used as a singular in English seems like special pleading to me. No English teacher of the last few hundred years would have taught that "they" is an acceptable substitute for "he" or "she". Certainly none of mine ever mentioned that it was once acceptable, but no longer is, and none ever spoke about it like a "thee" or "thou" situation either. Maybe my education sucked.
But correctly, I should have said "in my lifetime", or "for the last few hundred years", "they" has been singular. Any use of "they" as a singular was seen as either laziness or ignorance, and it was always "tsk"ed to high Heaven. So to be all, "We've used "they" as a singular since forever!" seems like special pleading. I mean, be fair, the writer dug up one example from a time when the English they spoke needs to be translated into the English we speak. To act like DUH, "they" has always been a singular option, comes across, to me anyway, as disingenuous.
I am not a grammarian (obvi), I'm really fine with an evolving language, and I'm happy to use whatever pronoun someone prefers, but now that we are at the start of a change, I am putting in my appeal for a different spelling -- stay with the they, but spell it "thei" or something. This will avoid the awkwardness that our lack of a second person plural sometimes causes. And with they acting as a singular, we'll have a new batch of "Is it they, they, or they, everyone?" questions that create confusion. We already have to contend with the "not you personally" stuff because of this, why ask for more.
And give us a second person plural in English, too. I vote for You all or y'all -- but plural, not singular! New can of worms. Le sigh.