Yes, most New York City movie theaters operate on Christmas Eve, often with holiday-themed schedules (early closures around 6–8 PM). Major chains (AMC, Regal, Alamo, IFC, Film Forum) and independents typically run reduced hours.
Always verify: Check the specific theater's website or app (Fandango, Atom) for showtimes and hours, as they can change yearly or by location. Christmas Day is universally open with full schedules.