It's clear that she isn't actually defending Mary Sues, but a different concept altogether. Honestly, she didn't really seem to know what she was talking about; she seems to be laboring under the (admittedly, unfortunately common) delusion that "Mary Sue" means "any female OC who can do anything" and is defending that concept instead. She's taking animosity towards a canon-warping, poorly-written monstrosity and thinking it's directed towards any and all female OCs, and basing her paper around that. Her thesis is based on a faulty premise, and if she really understood what a Mary Sue was, and what a Sue really meant, I doubt she would still be defending them.

She also didn't seem to realize that "A Trekkie's Tale" was an intentionally bad parody. So I'm not sure what to make of that.

My first thought is that I'm having a hard time taking this seriously, when they keep dragging in 'A Trekkie's Tale' to use as an example without really acknowledging the fact that the whole thing is a blatant parody. The way they write it, you would think that it was the first story about a female commander on the Enterprise, when it's actually a parody of something that clearly had already been going on for a long while.

That said, I just shrugged my shoulders at this. They obviously have a definition of Mary Sue which is different from both the one generally used on the internet and the one used by the PPC.
In their vocabulary, Mary Sue seems to mean any original character who is either a woman or belongs to a minority group, which is not adequately represented in the canon work. This includes canon characters who takes part in slash, which is something I have never seen in any definition of the term before.

But, from their point of view, where a Mary Sue is 'any independent female character in a male-dominated world', sure, it makes perfect sense to say that Mary Sues are empowering.
If we take the PPC definition which is closer to something like 'any female character who dresses like a dominatrix, insults Arwen, stuffs Eowyn into a plothole, makes Gimli a raging misogynist just to give her some opposition to overcome and who ends up winning the heart of Aragorn in spite of being a complete and utter brat', then no, I don't find Mary Sues to be the least bit empowering.
Barb Wire was a woman in a male dominated environment,who beat up men and objected to being called 'babe' and oddly enough, I didn't find her the least bit empowering either.

The authors of the essay seem to focus only on the fact that 'here's a minority in a heteronormative, male-dominated, predominately white world, whee!' and ignore the negative sides or these stories. People who are against Sue's have a lot of legitimate complaints about them and they just brush them off like 'oh, they're just mad that there's a woman in the fellowship, when Tolkien didn't write one in'.
Um, no, we're mad that she's ordering everyone around and is generally acting in a way that would never ever have been tolerated by one of the male characters.

Mary Sues do nothing to prove that women can be a part of the fellowship or command the Enterprise. Rather, they seem to support the idea that the only way a woman can do those things, is if all logic and common sense is revoked. I find them an insult to good characters in general and well-written female characters especially.

Whether Mary Sues are awful constructs of bad writing or unfairly demonized by prudish gatekeepers is an ongoing debate that pops up here every so often. A lot of people (not including Suethors) are not big fans of groups like the PPC.

I won't touch the fair use - making money off of fanfiction is something that I highly doubt will ever be legal (without the author's permission, or the expiration of copyright, or what have you), no matter what is claimed about the story.

But the Mary Sue, in some ways, and to quite a few people, is in fact seen as a symbol of empowerment. In some ways, I actually quite agree - not in the fanfic scenario, so much, but in original fiction. Let's try this one: a wealthy girl is orphaned at a very young age, and grows up to become one of the world's most unstoppable assassin-type vigilantes. She can stop any villain, and best any one of her teammates (with varying degrees of ease), her male opponents tend to fall in love with her, none of her female opponents can stand up to her for more than a story arc before getting curb-stomped, and in general, anyone who dislikes her is Bad, Very Bad Indeed* (and probably corrupt). She is the Best At Everything; her civilian alter-ego is rich, beautiful, and all the guys at every party line up to be with her... but she also has a Dark and Tortured side, which mainly comes out at night with her alter-ego. Her friends are devoted to her, no matter how badly she might treat them, and in the end, she is (almost) always proven to be right.

The Sue in question, of course, is gender-flipped Batman. I have exaggerated a bit to make a point, but do you see where I'm coming from? In mass media, male characters are 'allowed' to be over-the-top and perfect; female characters who do the same are Sues. Batman is, admittedly, a very over-the-top example. Let me point out this.

A blurb of a much longer piece. (The latter contains some NSFW language.) This just about makes my point. Not that a guy wrote a bad book. Not even that a guy wrote a bad book and got critical acclaim for it! But that I think it is pretty clear that if you just flipped the protagonist's gender... he'd be A SUUEEE OMG. (Like Eragon! Or, hell, Bella Swan!)

I am one of the weird PPCers who thinks Sues and Stus can be done really well - even fanfic Stus/Sues, on very, very rare occasions. I've had people argue before that if a character is written well, they're not a Sue. But honestly, I see that exception applied a lot more often to male characters. IIRC, people have called Alanna, of Tamora Pierce's Tortall canon, a Sue. I haven't really seen that applied to Harry Potter - though he has the same sort of striking eyes, supernatural-ish help, and accomplishes feats of great heroism etc, etc.

So... no, I don't think Mary/Marty Sue/Stus are really good things. But I don't think there's anything wrong with people using Mary Sues as a tool of empowerment, provided the characters are well done. One of the criticisms I've seen of Sue-hating is that the biggest beef seems to be, in many cases, femininity. For example, in A Song of Ice and Fire, Arya gets hella love from the fandom. (As she should!) But Sansa gets vitriolic straight-up hatred from the fandom - and, leaving aside her childish shallow issues (which, c'mon, look at the later books), seems to be simply because she's a girl. And unlike Arya, she doesn't try to be a boy. She does girly things. She's good at them. She's pretty, and she believes in the fairy tales involving a handsome and chivalrous knight, and for this she gets crazy amounts of hate.

It's not cool. And I don't think there's anything wrong with writing Wicked Awesome Girly-girl Feminine Characters who are Totally Great At Everything. Like male characters who are Wicked Awesome and The Manliest Ever and Totally Great At Everything, they need to have characterization. If they've got that, we've got no beef with them, I think.

(And, you know, spelling/grammar/etc. But that's what syntax-betas are for!)

*Depending on the writer, of course, as with most of these things - Nolan's Batman is a good one to substitute, here.