"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.