In the illustration you showed, the punching eye was above. “Punching down” refers to the practice of acting against people who are, in some sense, disadvantaged relative to the person acting. For example, in comedy, it is generally understood that it is unacceptable to make jokes about disadvantaged people. The image seemed to depict this.
As for the “gendered interpretation”, the eyelashes of the eye attacked are longer, and the defending hand appears more gracile, suggesting a feminine victim.
Of course, I could be over-analysing things here, a common fault of mine. These were just some impressions that came to mind.
