But how is that not inequality in action? Men are pressured to seek power while women are not or are not pressured as much or actually pressured not to seek power or some combination of that. In what way is that society still "egalitarian"?
That is a great question.
Its a difference, an inequality in the most absolute sense of the term. When you spoke of "inequity in underlying systems", I assumed you were referring to things of a more formal and institutional nature, the "system", not the vague workings of ingrained cultural pressures. The truth is that, taking that absolute standard to its logical extremity, an egalitarian society cannot exist unless every single person is treated exactly the same way, recieves exactly the same upbringing, exactly the same expectations, and exactly the same education. For good measure, eliminate all notions of "feminine" and "masculine", and the concept of race. Then we'd be sure that everything was equal because nobody would be treated differently, there would be no categories to lump people into. It'd be equal, but I'm not sure how many people would go for it. The problem is that even the smallest difference in treatment can be construed as an inequality if you try hard enough. Such social groupings have no place in a totally equal society.
For that reason, I have to see egalitarianism as a spectrum, and I think a society with the mentioned cultural pressures remains firmly within the spectrum provided there is no official or systemic limitations on individuals of said group based upon their group, those limitations not extending to cultural pressures unless they explicitly and vehemently discourage one group from opportunities another isn't discouraged from. I don't think that's the case here.