I don't know why some people have such stringent requirements on what is or is not a Christmas movie, but only when it comes to Die Hard. Does there need to be elves to qualify? Reindeer?
Home Alone is almost universally considered a Christmas movie, yet a kid could be left at home to deal with robbers any other time of year. Bad Santa is considered a Christmas movie but has no Christmas theme outside of the occupation of the main characters. I'd even argue that A Christmas Story could be centered around Ralphy's birthday and it wouldn't change the plot. It would only mean AMC wouldn't play it on repeat for 2 weeks leading up to Christmas.