To see why "No" is the answer, consider, for instance, a similar question, "Is your paranormal aura the same colour as your t-shirt?" (Answer "Yes" or "No".)
You can't correctly answer, "Yes it is," unless (1) you have a paranormal aura; (2) it's the same colour as your t-shirt. Of course you'd like to say you reject the question. But of the two answers allowed, "No" is forced if you don't have an aura.
Or, again, it's like the old, "Have you stopped beating your wife?" ("Yes" or "No".) ... If he hadn't ever beaten her, the answer he should give is, "No". (To answer "Yes" would be to allow that he had started beating her; you can't stop something un-started.) But that might lead people wrongly to think he was beating his wife, just as ONS thought people like me are trans.
Your description "... the epitome of bad question design" is wholly apt.
It's kind of sickening ONS (ONS!) got itself so captured as to offer a new paradigm for an illegitimate leading question, "Is the gender you identity as the same as your sex registered at birth?" to take the place of, "Have you stopped beating your wife?"