(Nice that you saw Over Sarcastic Production’s video, I may or may not have watched a good few of them.)
Honestly, I think I can agree that a Mary Sue is someone who the world distorts towards. Special ability? Dump it on the main character! Special plot scene with a huge climax? Let the other characters stand back, Mary’s got this covered! Aaaand you get the idea.
However, I’d like to bring up one of the best deconstruction of the Mary Sue archetype that I’ve seen - it’s not even a fanfic example here. May I bring your attention to The Legend of Heroes: Trails of Cold Steel, namely its protagonist, Rean Schwarzer. At first Rean can come off a bit as your typical Gary Stu - he’s kind, attractive, a bit of a chick magnet, he has odd superpowers, he’s even a chosen one to pilot an ancient mecha divine knight thing - but then this game decides to display the consequences of what happens when you gain so much attention. Kind and attractive with all the girls? If you play him as someone who tends to not hang around the girls, it can begin to come off as bothering and exhausting. Odd superpowers? For the first two games they do him nothing but good, but some the third game and he’s lost control of it, because it’s something he’s doesn’t understand, and the person who can control it is the main villain of that game. Ancient mecha divine knight thing? He’s become forced to use it in a war that he doesn’t want to be a part of, and now the whole world knows his name - and he’d rather just study with all his friends at school. It has a serious impact on his mental health by the end of the second game alone, but it gets taken to a whole new level at the end of the third.
Not to mention, he has ten other classmates, and all of them actually play a role just as big as he does. The glasses girl who gets all of the marks? A witch sent to watch over a trial in th school. The two boys who initially feuded non-stop? Their parents are the two leaders of separate factions, and both end up playing important roles as you would expect due to this. The two small girls with short hair? One is an ex-assassin, while the other is a literal result of human experimentation who is sent as a government spy. The skiving playboy? He’s the main villain! On paper Rean Schwarzer is a Gary Stu, but Cold Steel managed to deconstruct just what it means to be the centre of what’s happening - you get caught up in so much that you can’t keep track of it all, and you need to fall back onto those you trust just to keep you sane.
I mean, that’s more serious example of a well-written Gary Stu, if you even want to call him that. I think that in fanfiction (and normal fiction too, like non-Abridged SAO) something that people miss with a Gary Stu or Mary Sue is that every action has a consequence, and nobody can do anything on their own. The universe can’t revolve around one person because one person can’t manage the whole universe - like a supermarket brand has cashiers, shelvers, the higher-ups managing the money they use and so on in order to just make one supermarket branch, a fictional world needs multiple different components to make it run smoothly - and one person can’t run all of those components and make it seem real. With the previous example of Cold Steel, in the second game the main class is left with an entire flying ship to operate, and they need to enlist of the help of at least 20 of their other schoolmates just to make the thing run well. If Rean could just do it on his own, I wouldn’t be able to believe it for a second.
So that’s the criticial flaw of a Mary Sue - if you put all that responsibility onto one character, and none onto any of the other characters, that’s what creates that black hole effect. At least, that’s in my opinion.