So, here is why most "research" coming out of Schools of Business and Economics is such tripe.
They tend to be highly incompetent at thinking about complex causal models of human behavior and decision-making, leading them to simply throw in a bunch of "control variables" and presume that this is a more valid test of a causal hypothesis. Their naive faith in statistical modelling makes them blind to the theoretical assumptions that inherently underlie their interpretations and their choice in how to set up their statistical models.
Valid control variables are those that plausibly cause (even if indirectly) both the other key variables of interest (gender and compensation), but would not plausibly be a mediator or interact with the causality between the other variables.
For example, number of criminal assaults and ice cream eating are correlated. A valid control to test whether ice cream increases assaults is air temperature, because temperature can indirectly cause both things, but is not a plausible mechanism or context that determines when and how ice cream causes assault.
In contrast, age and experience are actually not something you can simply control for to test whether gender impacts salary and promotion.
Neither age nor experience cause gender, so they cannot be a third variable explanation, which is the main justification for controlling for a variable. Instead, gender could actually causally impact the average age and experience of people within a given company, and it can do so via sexism. Gender can trigger sexist mistreatment that over time leads to quitting, which would produce an average lower age and experience level among the women who remain. In addition, gender could causally interact with age such that the kind of sexism that leads to quitting is most targeted against older women and not the young (hot) women in a company. Thus, the older women quit more both because they mistreated more than young women or men of any age, and because as women gain job experience they also gain more and more sexist experiences that eventually lead to quitting.
Of the subset of women that are left, they are non-representative and could easily be the type of women who persists despite constant decades of sexism, including being so confident that their skills are much higher than their male supervisors that the sexism is not enough to deter them. Their added obstacle would mean they are more committed and competent than the males promoted around them who did not face this obstacle. Thus, explaining their higher pay. Yet, their success does nothing to diminish that they were targeted by sexism as were their female coworkers, many of whom dropped out just as many men would have had they faced such an obstacle.
Note that while this is speculation, so is every conclusion in the OP article. Correlational data, no matter how sophisticated the analysis means nothing without interpretation that is always speculating about the most plausible underlying causal relations that could explain the statistical results
My speculation seems to account for their results equally well, and is more psychologically plausible, taking into account how other data speaks to the likely way in which age, experience, and gender would relate to each other, if sexism did exist in the workplace.
These researchers are assuming that the only way the gender would impact age and experience is via non-sexist factors like desire to be a stay at home mom. Only if that untested assumption is true, is there approach valid. And there is evidence that it isn't true. Women quit due to sexist treatment, and that would make those still on the job at any timepoint younger and less experienced than people who don't quit due to sexism, men.
