Let me see if I can back this up to the original point, because I think I know the phenomenon being talked about and it grates on my nerves like nobody's business too. I've never watched Ms. Sarkeesian's videos and don't plan to, but I think I know what's being discussed.
The problem is all because of this oversimplification that "power = masculinity", and the reverse that being feminine CAN'T be powerful.
It's kind of like somebody prattling on about how they "aren't like those other girls" because they don't wear makeup and watch Dr. Who and play video games. At first glance it might seem on the surface like a positive step forward if someone is proud about giving up those 'traditionally feminine' qualities and remaining a girl. However, there's still a big problem - and that is that when you do that "I'm not like those other girls!" thing, you throw other women under the bus. If you say you're "not like those other girls" because you're intelligent, you're really saying that all the other women are unintelligent, etc. etc.
This trope kinda does the same thing. It directly correlates having power, having battlefield prowess, having physical strength, kicking ass, having agency, being able to affect what's going on in the world around them, etc etc with... having masculine characteristics. That means they're also making the point that if you DON'T have these masculine characteristics, you can't have power, can't have battlefield prowess, can't have physical strength, can't have agency, can't affect the world around you, and can't kick ass.
Then it's just the same ol' same ol' bullshit wrapped up in a new package.
I'm not going to begrudge every female character that has masculine qualities for this. I think if people stop and make the character have reasons and depth, this can work. However unfortunately a lot of people don't go that far, and just put up a female character with the depth of a cardboard cutout, and go "look! she's empowered! you can tell because she's manly!". And that makes me want to bash holes in the wall with my head out of sheer frustration.
There's more than one way to be a girl, and you can have agency and be powerful many different ways. Not just by being like a dude.
(Unfortunately, when a lot of dumb writers try to make a girly girl that has that agency, they end up with something also detestable - because they think the only two states a girl can be are "manly" and "very fuckable". They think the only other way to be a woman is to be appealing to them and to be sexually available to them. Then you get a cardboard cutout character with zero depth that's just an insulting parody. The true solution is to stop thinking of women as weird strange things and to actually write them, design them, animate them etc. as PEOPLE, with DEPTH and REASONS FOR THEIR ACTIONS, but that is sadly pretty uncommon in media these days. It sucks. And that's kind of another topic anyway, lol.)