Well, yes, but her opponents are also dismissed as "macho loudmouth[s]", which is something you can only really say about a man.
That's not to say that all of the criticism of Mayer is fair or justified. I imagine that very little of it is. But I suspect that she's being criticised much more for having ideas, and the will to pursue them, than she is for being female (say, an 80/20 split). But it's a lot easier for people who don't care about the intricacies of Yahoo's product strategy to talk about her gender than it is to talk about her ideas for Yahoo's products.
I think the language is indicative of an entrenched male culture at the top trying to cope with a strong female leader from the outside. It's kind of the worst of both worlds. Sure, being a woman isn't the only thing, Mayer is also in tech. Top management probably finds that weird, too. However, calling her things like "a princess" or "stuck up" is incredibly patronizing and sexist. Everybody knows those words pretty much don't apply to grown men in a situation like this. That's to say, given the set of circumstances the semantics of these labels are specific to her gender.
I can't help but think people take issue with her gender, and then criticize her on the product front specifically so do they don't look sexist....which is why you see all this criticism that lacks proper justification about her strategy at Yahoo.
I don't think people criticize male CEOs as much for "having ideas and the will to pursue them." You can't say there isn't a gender-based double standard for CEOs obsessed with product to the degree that they sometimes offend their employees. Steve Jobs was known to berate and verbally abuse his employees, but people excused it because he was a "genius" and a "visionary". Meanwhile, the worst Mayer has done is ask work-from-home employees to return to the office and people call her a "princess".
That's not to say that all of the criticism of Mayer is fair or justified. I imagine that very little of it is. But I suspect that she's being criticised much more for having ideas, and the will to pursue them, than she is for being female (say, an 80/20 split). But it's a lot easier for people who don't care about the intricacies of Yahoo's product strategy to talk about her gender than it is to talk about her ideas for Yahoo's products.