I think that no one here can accuse me of having any affection for Kylo Ren but to call that sad piece of writing a Gary Stu? Now that's beyond my comprehension.
A Mary Sue is a character who fails almost at nothing, that everyone loves, who doesn't face any challenge she can't easily overcome. Long story short, Rey. (there is also the very important fact that a Mary Sue says a lot about her writter but i think that this aspect of a Mary Sue is less true outside of the book format)
Now, let's take a look at captain emo. He fails constantly, not even his parents think he's worth anything and there isn't a challenge he managed to overcome without any form of help.
The dude is a failure. Which would have been interesting if written in a better way but here you go...
If anything he is the anti-gary.