The idiom isn’t gendered, a component of it is. Likening someone to ‘the little dutch boy with his finger in the dyke’ makes no claim on the gender status of the referent and is equally applicable across all genders. If they insisted on calling you Mr. Egon, then sure, that’s misgendering, but ‘go off king’ is a established turn of phrase that I have also seen generically applied because it likewise makes no claim to the gender status of the individual referred.
The only way I think it can be construed as misgendering language is if the parts of the idiom or turn of phrase are parsed individually, which is exactly the opposite of what you’re supposed to do with an idiom.
If this sentence is misgendering myself, then I’m the Queen of England. I get that this guy is a shithead but pretending that he’s also doing something wrong here seems to be playing for some esoteric own.
I’m not saying it’s not a thing, but I have literally never seen it used, and I couldn’t find an ngram viewer with a corpus end date after 2019.
It would never occur to me to say “go off queen” , in much the same way it would never occur to me to say “yass slay king” regardless of the gender of the referent, making them both gender neutral in my use.