I'm not sure we're reading the same article, throughout the article her central point is that women self-silence, doubt themselves, and so on, and she claims the internal barriers are "one of the most persistent" and argues women need to do more to work on themselves - the central purpose of the article is to argue this point ...
And yeah, I think "ambition" here is a euphemism for the socialized, masculine trait of over-competition. Actual ambition is obviously not masculine or feminine, but in the context of women being shut out of leadership and drowned out in meetings or debates, the "ambition" she is talking about that women supposedly lack becomes willingness to talk over others and be anti-social, to put others down. Having been a STEM major and spent decades in offices where meetings are conducted according to who can be loud and rudely interrupt the most, I do tend to think this kind of ambition is masculine. But unlike the author, I think the problem is with that toxic culture, not with women.
I would like a culture where people are humble and kind, and where people are given the ability to speak even if they don't interrupt or exude confidence. My point is that the values she thinks women should embody are one-sided, and while it's fine to suggest some women should be allowed to pursue joining the boy's club, I think the problem is more with the fact it's the boy's club than with women's difficulty with embodying that boyish behavior that grants them entry.
This doesn't mean her experiences are not valid or should be discredited, but I do think she draws the wrong conclusions (and yes, I do think this is a common, almost stereotypical, situation - physicists and scientists make poor philosophers and sociologists, and yet they feel confident to jump in anyway).
Even her article seems in tension, she admits the problem is external:
External dynamics, interruptions, dismissed contributions, or condescending explanations further erode women’s voices. The final frontier of gender equality may not lie in law or policy, but in these subtle, corrosive habits that continue to hold us back.
But then brings it back to the individual and internal in the end.
I guess it's fine, this is a commentary article anyway - it doesn't have to be perfect or consistent, but I guess you saw my reaction because of how personal this is for me. I'm so sick of the corporate culture that promotes toxic values, and I feel like she embraces that rather than calls for a change in the culture. It feels very Lean In to me.