That's not sexist though, it is just equivalent to noting she's a woman (like calling her "her" and "she") because we can reasonably offer the same criticism about a man. A man can have an extremely arrogant demeanour instead of the controlled gait and bearing proper to the stronger sex. And adjusting for language drift people do make that sort of complaint of men, I remember one criticism of Biden being that he walked in a frail way and fell over a lot - literally complaints about his gait and bearing giving a bad impression. Not a very strong criticism but he was male and it was made.

We might reasonably infer that she got called arrogant for doing something that wouldn't be considered arrogance in a man, the article has unhelpfully elided that detail (maybe the original author did as well). But we've also got to admit she might have actually been unusually arrogant, that does happen from time to time. If I were in charge of a military I'd be standing around even more arrogant than I already am.

pjc50 offered a good example of something that was actually gendered - women not being able to own property in their own right for whatever unfair reason. The quote isn't that sort of out-and-obvious sexism. Said quote could almost be modern political whinging.

PS I'll add in an acknowledgement that words did mean different things back then so possibly at the time the only reasonable reading was with an "[as with all women]" on the end, but the fact is that as written this quote is making specific accusations of arrogance and arbitraryness that are not contained to either gender and are bad in all leaders, female or otherwise. He didn't write "women are all arrogant" or "women are all arbitrary". If anything the thrust of the quote is most women weren't either of those things. It doesn't support the idea of double standards or ludicrous criticism that would never be made of a man.