Women can absolutely be sexist towards other women-- as in a jealousy scenario. Sexism is being targeted because of your gender. The fact that this is not obvious explains a lot.
It doesn't matter whether the source of that sexism is the way the men treat women, or whether its the way a high-powered woman treats the other women. (Both are at play in this particular story.) If someone is being discriminated against due to their gender, the company culture has an issue with sexism.
I brought up jealousy as an example, but I didn't mean it to be romantic. It can be an issue of feeling threatened by another woman, as when a woman used to be the only female voice at her company. It's a twisted perspective, but there's data to say it exists.
It's sexism if a human being[1] is being mistreated, harassed, or "labeled" because of their gender[2].
It's perhaps easier to understand from analogy[3], take a look at racism[4] and see if you can find any similarities.
Feel free to ask any question if something is still unclear.
[1] https://simple.wikipedia.org/wiki/Human_being
[2] https://simple.wikipedia.org/wiki/Gender