Well he is an economist so he is saying he is paying them the market rate which he believes to be underpriced relative to their intrinsic value. As an economist he would place the underpricing blame on society and the labor market. A similar situation would be if a company realizes it can get more value out of hiring junior developers cheaply over senior developers. An economist would also say they weren't underpaying the junior developers because no one else was willing to pay them more.
I think he's claiming his competitors are overpaying men by artificially pretending supply is half the size it actually is. Or looked at another way, the market value of men is determined by companies that hire everyone + companies that only hire men, but the market value of women is determined only by companies that hire everyone, so demand is lower. Either way, it's not "underpaying" relative to either intrinsic value or value in a fair (everyone is willing to hire everyone) market, which is most of the moral argument for why underpaying is bad. It's "underpaying" in the strict technical sense of paying less than what others are willing to pay men, but that only applies in the hypothetical where one single woman were being hired as if she were a man; if all women on the market were hired like men, supply would increase which would affect everyone's pay.
I think there are multiple solutions to a gender wage gap resulting from markets with irrational participants, and reducing the market value of the overpaid gender is a perfectly valid way to accomplish it. I think that's what he's doing.
By hiring women he's reducing the supply of women in the market which presumably raises their value, but I do agree the more progressive approach would be to hire women for the value he would be willing to pay men
Note that he's not necessarily willing to pay men more - the reporter says the senior staff was "mostly female," not balanced. He might have just been willing to pay men and women the same salary, which was less than what other companies were willing to pay men.
Not necessarily. He could be underpaying everyone. In which case, the degree to which women accept offers vs men would contribute to a systemic pay gap, without directly intending to.