Nope, that's not supposed to be the devil, or even that Tim Curry villain from Legend. It's the Krampus! According to the legend, the Krampus is the monstrous creature that accompanies St. Nicholas on his annual sleigh ride around the world in order to warn and punish all of the world's naughty children as St. Nicholas rewards the good children. He may only be one of St. Nick's many companions, but he is certainly the most frightening.
He gives those song lyrics a whole meaning: Oh You better watch out, You better not cry, You better not pout, I'm telling you why. Krampus is coming to town!