I play through Arkham origins every year because it’s based around Christmas and has a cool haunting soundtrack to go with some joker one liners that really make the only christmasy game I can think of.  Are there any other games, from past gens or recently, that have that Christmas story/vibe?

Not exactly a Christmas story, but Shenmue does have a few characters dressed in Santa hats or something around December 25th in the story.

Kingdom Hearts 2 (and I think 1 as well IIRC) have levels from Nightmare in Christmas, with the second one having Santa and Christmas town.

There were a few Home Alone video game tie ins, so I'm guessing those should count.

Nights into Dreams had a Christmas version.

There's Elf Bowling which I'm pretty sure was released on DS and Wii.

Then there's whatever this is... https://www.youtube.com/watch?v=JoYg5_7iKac

Mario & Sonic on the Olympic Winter Games are fun to play around Christmas. They're fun and lighthearted games, that obviously take place in the snow.

(They're not about Christmas, but they do have strong Christmas feels.)