I don't have much time for EW and her comment was fairly shallow.
I think Bindel is being unfair though and maybe deliberately so. I don't think Watson means anything like "pull yourself up by your bootstraps". I think her intent is to support policies that would, for example, give more choices to a woman stuck in an 11th floor flat with her three kids. Be it free education, social assistance, daycare, whatever.
Without something more specific than "empower women" it's not that useful a statement, and there are lots of questions about any policy approach. The stuff about armpits is naive, as if people just aren't affected by social norms. The idea of freedom being about choice can be challenged on a basic level, too.
But Bindel is leaping to an interpretation which I don't think she would if someone else said it was important to empower women.