The Nightmare Before Christmas may not convey the same emotions that a traditional Christmas movie does, but it’s a Christmas movie nonetheless. The vibes may be spooky, but the themes are of redemption and the recovery of innocence, as well as, family and home which are common themes for Christmas movies.
Also we cannot ignore the fact that the movie is all about stealing Christmas and making it scary, but it is still Christmas. A holiday does not change because Jack Skelington wants to take it over and makes it miserable for everyone. In the end, Jack needs to learns the true meaning of Christmas.