We have gone over this multiple times. Economic analysis that enter all kinds of control variables for correlational data are of valid causal attributions for the observed pay gap difference. They cannot tell us that the gap is due to something other than discrimination. They can only tell us that the data that is available does not allow us to attribute it to discrimination or to other causes.
The problem is that the people who do such research so frequently ignore the massive biases they are imposing on their interpretations via their presumed causal relationships.
In this case, a major presumption is that time in the workforce can only be a cause of pay differential and not an effect of pay differential. If women are discriminated against for being women by getting lower pay they are more likely to leave a particular job, a field of work, or either reduce their work hours or the workforce altogether and let their husband who get more because he is a man work while she raises the kids. All of these factors, which can be effects of getting lower pay, would wind up manifesting themselves as "less hours per week" and "less time on the job", which are the primary variables that the researchers are attributing the wage gap to.
Their economic analyses are incapable of distinguishing this causal pattern from these researchers assume is possible, which is that the women are paid equal but choose for their own various reasons to work less, switch jobs, leave the work force etc.. When you enter these variables as "controls" in the analyses and the most of the wage gap "goes away", that is what would happen for both of these causal scenarios.
BTW, this abuse of multivariate correlational analysis is not limited to those trying to discount gender discrimination in pay. It is a rampant problem in the social sciences where researchers, who were never trained in actual experimental scientific methods which allow for causal inference, learn complex statistical approaches to correlational data and get deluded into thinking they can use them to "reveal" the true causal relations among factors, which they cannot.
All these methods can do is show you patterns of shared and unshared variance that you then must interpret in terms of its consistency with the patterns predicted by various possible causal models. The number of and reasonableness of the possible causal models you consider will determine the validity of your causal inferences, which in most cases of non-experimental data can never be made with more than modest confidence.
In sum, what the OP and the Feakonomics data show is that the wage gap is AS consistent (not more consistent) with the cause being hours and time on job versus discrimination with those variables being effects of discrimination and partial mediators of discrimination.