I do question one of the examples a bit. The idea of giving advice to female founder to step down as CEO in favor of a male cofounder sounds like bad advice. It's pointing out one rather drastic solution, rather than the actual problem. Better advice would be to lay out the observed issues and help think through a range of possible solutions, if everyone can get on the same page about the problems. Maybe the solution would still be a change in roles, but there's a lot less chance it would seem sexist the advice were predicated on a lot more information.
I guess it depends on your definition of sexism. Reading these comments, and just general life experience, I believe different people have different definitions of what sexism is. Regardless of company policy or the law of your country.
Taking your definition of sexism I would say every interaction with a woman is a form of sexism. Everyone, at all times, tries to speak to another human being in a way that conveys a message. That manner of communication changes based on social norms. Which, as this article points out, currently seems to be differnt between the sexes.
Generally I believe people do try to "talk to their audience".
One example from my life: if I notice my colleagues have nice shoes, I point it out. If it was a female colleague, I probably wouldn't because of the risk of that social interaction "going wrong".
Someone could point out that complimenting someone on their footware is weird/wrong/shouldn't be done during working hours. If this is the case then I'm not talking sport or politics or local news or how you're kids are doing...
I think the article does a good job highlighting the downside of being hyper-aware of the social situation around a person trying to convey a message to another person, and how that could be labeled as inappropriate.