I think “I am no man” is a perfectly good explanation in the movie. It implies that the witch king is relying on a prophesy he doesn’t fully understand (rather than a spell). “If Croesus goes to war, he will destroy a great empire.”
There's also a strong tie between this kind of prophecy and Tolkien's (and Anglo-Saxon literature generally's) love of the riddle form; "riddles in the dark" draws clear inspiration from Vafþrúðnismál, which doubles as both prophecy and riddles. Along these lines, I also recommend Adam Roberts's The Riddles of The Hobbit.
