The list is of Christmas songs, not Christmas carols. Christmas carols are a subset of the broader category of Christmas music.
All of the songs listed are, by any reasonable definition, Christmas songs. "Grandma Got Run Over By A Reindeer" is a Christmas song.
Calling it a carol would be a stretch, I'll give you that. :-)
I guess our problem is that we expect more from the “things” attached to our most important holiday. You are right, I mislead myself concerning the difference between the two. But Christmas songs like these, in my mind, are just for making money and not celebrating the greatest of days in our earth’s history, the birth of the Lord. I might be a wee bit stubborn on any other approach other than true love of the event and not the residual that can be scraped off of it. My apologies. I guess I’m a little selfish.
rwood