I know there aren't that many, but at least there's a few. I'm not including games that take place during the calendar year either in real time (like Animal Crossing) or not (like Persona).
Christmas NiGHTS into Dreams: pretty self-explanatory, it's also included in the later console ports, although it's missing the cool presents you could get, including being able to play as himself.
James Pond 2: Codename: RoboCod: takes place in Santa's castle and you have to save Christmas.
Yakuza: surprisingly many of them take place at Christmas.
Daze Before Christmas: a platformer for the Mega Drive and SNES that's not particularly good.
Xmas Lemmings: basically demos of Lemmings with Christmas-themed levels, there were a bunch of these for PC and Amiga.
Tyrian: Originally a DOS shmup that was released as freeware and now has open source ports, there's a Christmas mode that activates if the system clock is set to December. I'm pretty sure there were other DOS games with Christmas modes too.
Duke: Nuclear Winter: a Christmas-themed expansion for Duke Nukem 3D.
I also forgot that Batman: Arkham Origins was a Christmas game, and Jazz Jackrabbit 1 & 2: Holiday Hare, even though I had a list of games and that was on there.
Doesn't it also have a Batman/Joker Pieta-ish image somewhere towards the end? I can see where that all blurs together as "Christmas" in my half-remembered memories.