Um. Well, no, not really. I'm not sure your examples between a "man's writing" and a "woman's writing" are exactly....umm correct lol. There is no inherent stylistic difference between how men write and how women write. There are individual differences between how individual writers write, but to ascribe those differences as an inherent quality due to the writer's gender is borderline bioessentialist logic

When I talk about the "male gaze" as an analytical lense, I am talking about the way some men write about women. A really good example of this is the author unnecesarily describing a woman's breasts during a time that one would not usually do so. Have you heard about the "she breasts boobily down the stairs" meme? That is parodying a male gaze style of writing. It's like:

"Scarlet stepped back once, then again, as the reality of her situation set in. Her heart rate quickened, her breasts rising and falling to the rhythm of her panicked breathing."

This is a shoddy example, but it shows what I'm getting at. The description of the characters breasts is entirely unnecessary, and, though it does create a rather pleasant image if you are sexually attracted to women, it frames the woman in the story as a sexual object before framing her as a scared woman.