Probably should have clarified my point: When I say that sexual objectification is generally gender specific, what I mean is that it targets one group (mostly women) in order to benefit a different group (mostly men). If violent video games were mostly marketed to and played by women, if it were mostly women making decisions about what wars get fought and who goes to war, or if it were mostly women who inflict the violence sufferered by many men, you'd have a stronger point. The point is not that video game violence inflicted on mostly-male mooks is inherently less bad than sexual objectification; it's simply that it is not a direct male analogue to sexually objectifying imagery of women. There are conceptual differences here that tend to get lost in these conversations.
As far as why most mooks are men, there are a lot of reasons for this. Part of this is that historically, men have had more access to the public sphere, where most violence takes place. Also, when you're using violence as a form of entertainment, it's often convenient to use as targets members of groups who aren't perceived as vulnerable. This is why you never fight against child soldiers in games, and why so many bad guys in books, movies, etc. are rich business men. If anyone suggested that media is 'oppressing' corporate executives by portraying them all as slimy jerks, it'd be hard to take them seriously. And I suspect that it's for similar reasons that people don't get too up in arms about men being objectified in movies and games by being portrayed as targets for violence. If games tended to play up the characteristics of men that can make them vulnerable to violence (i.e. You're shooting at mostly poor, conscripted minorities), then you would get a lot more complaints.
EDIT: Added some stuff.
I have a great deal of difficulty with the position that there is a meaningful distinction when media is targeted at a particular group and developed by that same group. And the reason for this difficult is, as I say above, because it ignores the intersectionality of gender, race and (especially) class. The men who make the game are not the same as the men who consume it and not the same as the men who benefit from the social hierarchy that produced this default template. It also ignores how this portrayal has negative impacts that in some ways parallel the negative impact on women. To me the issue with the sexualisation of women - and what makes it distinctive - is that this is tied to the type of historical disadvantage faced by women and is part and parcel of how women have been excluded from the power hierarchy for a very long time in our society.
Let me use a different example: I don't think that the portrayals would be the same even if it was women making a game for women using men as disposable mooks. And that's because of the historical disadvantage point. I don't want to be taken as condoning this hypothetical game - it would be bad. But I don't think it would be bad in the same way.
This is - in a way - the same theory tied in with the argument that there is something different about how roided out men impact male body image (because they're the power fantasy of other men).
I guess I'm not really disagreeing with your first paragraph (since I agree this isn't an apples to apples comparison anyway). I just happen to disagree with you on the "why" of it.