I don't know why this keeps being said when there is clearly a figure parallel to the Night King in the books:
https://awoiaf.westeros.org/index.php/Great_Other
- The Night King from the show is the oldest, most powerful, best, most badass, leader of the White Walkers;
- The "Great Other" from the books is an "Other" who is so special that he is called "Great".
From the show, we know that the Night King literally created every single White Walkers. He was the first and he created the entire race, by kidnapping children and turning them into his minions. That's why they were all destroyed when the Night King died. Beric Dondarrion even stated that the Night King "turned them all".
In that earlier quote I gave you from the wikia, you can replace "Others" with "White Walkers" and "Great Other" with "Night King" and you literally get the situation from the show.
The above quotes prove that this Great Other is not some astral entity that doesn't exist, he is present physically on Planetos and is gathering his forces Beyond the Wall, to prepare for the Great War. Like the Night King had been doing for seven seasons.
GRRM wanted Arya to kill the Great Other and end the Long Night. He watched the reactions to 8x03 and realized that everyone sane disliked the idea of the big bad dying to a ninja teen, so now he's in a writing corner and doesn't know what to do.
What's funny to me is that some GRRM fanboys claim that DnD ruined the White Walkers, that they are not supposed to be just a weapon created by humanity in the books. Well, Melisandre literally called them "children" of the Great Other... it's clear that the origins of the White Walkers are the same between the mediums and they were both going to be defeated in the same way (by taking out Night King/Great Other).