The creators of Game of Thrones have long flagged this as the Night King’s motivation. Back in 2016, D. B. Weiss told Deadline that the Night King was just “death”:
“I don’t think of the Night King as a villain as much as, Death. … The Night King doesn’t have a choice; he was created that way, and that’s what he is. In some ways, he’s just death, coming for everyone in the story, coming for all of us. In some ways, it’s appropriate he doesn’t speak. What’s death going to say? Anything would diminish him. He’s just a force of destruction.”