Even though the term has been somewhat bastardized into "sexual objectification" in general, "the male gaze" originally specificallt describes the trope of straight male cinematographers/directors literally framing camera shots differently for women.
The whole point is that the director (traditionally always a man in mainstream movies) views the character/actress as an object of sexual desire, and the camera - and by extension the audience - sees the woman through that lens. Literally forcing the audience to gaze from a straight male POV. This is an inherently sexist and heteronormative, usually subconscious process.
Now I do enjoy seeing Henry Cavill shirtless in a bathtub, but that's not the (fe)male gaze because the director wasn't imposing their personal bias, they were making a conscious statement. It's objectifying fan-service but not sexist nor heteronormative.
I suppose you could argue that the female gaze does exist in media where the authors are overwhelmingly female, such as the boylove genre. But that doesn't apply here because Shen's character here is literally a presumed straight man.
I get what you're saying but what I'm trying to get across is that "sexy" and "objectifying" are distinct from "gaze". It's about the translation of the author's desire into the framing of the scene. I doubt that Babish is attracted to himself in that way, he just framed it in a way that makes sense with the constraint of not wanting to show his face.
It's semantics, if you want to use objectification and "male/female gaze" interchangeably that's fine (though I'd prefer not to use a gendered term if we're talking about a phenomenon that's not inherently gendered).
But Shen used "female gaze" correctly in the original sense of the phrase here so I don't see why people are getting mad that he didn't objectify the guy as well, it's obviously not a comic that's meant to be read as "female objectification is cool".