When this video first came out, it was behind a paywall; so all I saw of it was clips posted on YouTube, and maybe other places. I also saw a few videos of Walsh commenting on it or defending it. Now, I have no interest in seeing it, because I think I have a good handle on Walsh's point of view.
(Sidebar: I used to say that I wished for the opportunity to address these matters with Walsh, and people like him, because they are practicing demagoguery with nothing more than rhetoric. Their arguments can be taken apart fairly easily. But it seems to me that Walsh picks and chooses who he interviews and what speech of theirs he will permit; and you can't have a discussion with someone who does that. You also can't have a discussion with a demagogue, a rabble-rouser, who has no real interest in "discussion" because he believes he is already in possession of The Truth.)
Walsh's question is easily answered, just as his wife answers it in the end: a woman is an adult human female. The question is, what is a female? or, what does it mean to be female?
Unless Walsh is going to retreat to a circular definition, I think his best response to this question is biological; and this leads to two further questions, based on whether Walsh is a materialist (i.e., believes that human beings are nothing but meat machines) or Walsh possess some kind of belief in a non-material aspect of humanity.
In the first case (which seems odd, if Walsh is a religious man), we can ask whether all that can be known about human biology is already known, or if there might be something more about human biology to discover. I would not expect him to choose the former point of view, because in doing so he would claim omniscience, for either himself or the current state of science as a whole. This means he is forced to concede that there may be more to femaleness than meets the eye -- something in brain morphology, perhaps. The fact that we have no proof, as yet, is not conclusive; absence of proof is not proof of absence, something, ironically, that these people frequently seem to forget. This means the answer to his question is a matter of belief, nothing more.
In the second case, then the question is whether or not it might be possible for femaleness to be at least partially non-material -- which, again, without claiming omniscience, Walsh must admit to. And, if this might be possible, the next question is whether or not this non-material aspect of femaleness and the material aspect of femaleness might diverge -- again, something he cannot answer definitively without claiming omniscience. And this, too, means the answer to his question is a matter of belief, nothing more.
So, it is apparent that the answer to Walsh's question, "What is a woman?" comes down to a matter of belief. And that's fine; the same thing is true for us. I believe I'm a woman, Walsh believes I'm not; and neither of us can prove it. What now?
Now, in a free society, we must each let one another believe as we wish and live accordingly, so long as we each don't interfere with the other's right to do the same.
There is a bitter truth here, which we must admit, if we are ever to resolve the conflagration currently sweeping the country: both sides are guilty of trying to legislate their beliefs. People on the Right are doing it now; but trans activists have been doing it for years.
This is a quasi-religious conflict; and both sides need to stop. Both sides need to stick to what they can prove -- such as the need for medical treatment for gender dysphoria. We can prove that, and the Right is trying to take it away based on their beliefs. When we get to court, this is one of the arguments that should be made: that science is on our side, while the Right's beliefs are on the other. So long as the courts remain rational and committed to the rule of law, we should win, hands down.