Redlambs
Creator of the Caftards comics
"A Mary Sue is an idealized and seemingly perfect fictional character. Often, this character is recognized as an author insert or wish fulfillment.They can usually perform better at tasks than should be possible given the amount of training or experience, and usually are able through some means to upstage the main protagonist of an established fictional setting, such as by saving the hero."
So, this is the "official" definition of a Mary Sue. With that established, I think it's easy to see whether she qualifies.
1. A seemingly perfect character. I think it's quite easy to agree that Arya is not a perfect character. She's done plenty of questionable, cruel or dumb shite during the course of the show.
2. Wish fulfillment. I dunno, who's wish is it that a little girl kills the night king? Even if people do wish it, it's because of her character arc, not her age / sex / whatever.
3. Perform better tasks than should be possible due to training etc. At some point I wished they would cool it with the endless fecking Arya training to be a good fighter montages. If anything, she's had too much on screen training.
4. Upstaging the main protagonist. Who is the main protagonist? I thought it was Ned, than Robb, maybe Danaerys? I suppose you could say she upstaged Jon? Jon is a daft cnut who knows nothing though, so who cares.
The only valid Mary Sue complaint would've been Sam killing the night king.
You really should look into it more. Not having a pop, but you've literally just posted the first response on google.
Not sure what definition you're basing that on as the term can include a lot of things and has evolved over time.
In general though, it's to do with a character having no flaws or being too perfect/powerful. I don't think you can apply that to Arya. I mean, in the same episode she got herself cornered, looked terrified and needed saving by two other characters.
But she was good at everything from Art to Zoology. We saw Arya's needle point and her drawing of a spear. She's not good at art.

Arya was excellent with a Needle!