Maybe winding stairs are traditionally built to wind one way (clockwise?) and the stairs in Cirith Ungol wound in the opposite direction?
That comment in the film was inexplicable. It doesn't appear in the book from what I can see.
The book describes Cirith Ungol to have its back against a cliff with a steep stairwell. It was built by Gondor to keep Mordor's forces in rather than out. That may be the explanation of the quote.
Here's an article why medieval staircases were built clockwise.