Die Hard is a movie where it being Christmas is relevant to the inciting incident but not intrinsically tied to the concepts of Christmas and is not 'a Christmas movie'.
We watched A Creature Was Stirring the other week, which was touting itself as a new Christmas horror movie, but absolutely no part of the plot would actually been affected by it taking place at Christmas despite the set being decked out in trees and garland and other seasonal trappings. Die Hard does use Christmas as a jumping-off point, as it exists it actually matters to the plot but could have easily been written any other way. Christmas is Die Hard's appendix; you could surgically remove the Christmas from Die Hard and it would have a decent chance of still living a full, rich life.
Gremlins, however, is a Christmas movie. We should all be watching Gremlins.
I hear this a lot about Die Hard but even the most dedicated movie critics seem to miss that John McClain is a Santa allegory.

