That really is the elephant in the corner: the variations in privilege by gender for the white university-educated middle and upper-middle classes are barely a rounding error compared to the gulf in privilege between them and the working class, or the non-whites even of the middle class, which the framework of analysis used by their article glosses over. That is why, outside of their bubble, cries of "male privilege!" ring so hollow. Nobody likes to be lectured by someone who spends more on a coffee, than they earn in an hour. Or who drops a quarter-million dollars on a degree of no vocational use.
I don't agree with most of Marx's conclusions, but he was absolutely right in that class is the lens through which to understand societies.