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).
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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
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James Pond 2: Codename: RoboCod: takes place in Santa's castle and you have to save Christmas.
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Yakuza: surprisingly many of them take place at Christmas.
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Daze Before Christmas: a platformer for the Mega Drive and SNES that's not particularly good.
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Xmas Lemmings: basically demos of Lemmings with Christmas-themed levels, there were a bunch of these for PC and Amiga.
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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.
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Duke: Nuclear Winter: a Christmas-themed expansion for Duke Nukem 3D.
Lifeline: unique PS2 game that you use a microphone and voice commands as your controls. You give voice commands and control a waitress aboard a rich space hotel that's taken over by aliens during Christmas time and have to survive. Also Mansplaining: The Game.
Blue Stinger: kino
Raw Danger and I think some of the Disaster Report games takes place during Christmas. Absolute cinema choose your adventure. A natural disaster befalls you and you must survive. Some of the choices you can make are absolutely psychopathic and funny lmao.
Parasite Eve is either a Christmas game or a New Years Eve game
PS2 and Dreamcast had amazing B-tier movie-like games that are Christmas games.