… pitching black ropes of it over the side …
The word sick is sometimes used as a noun to mean vomit, although it's more common in the UK than the US.
Although I can't find any direct reference to the phrase, there is the phrase ropes of vomit. It's used when somebody is particularly ill.
I did find a reference to the descriptive use of the phrase from "Kevin McClintock: 'The Thing' a masterpiece of a novelization" (emphasis mine):
In all my years on this earth, only two movies have scared the absolute you-know-what out of me.
William Peter Blatty’s “The Exorcist” is one. It’s still considered one of the most-frightening movies ever made, standing right up there next to “Halloween” and “Silence of the Lambs.” I was too young to see people faint in the theaters when Reagan brandished her bloody crucifix, and I never got to see the ropes of vomit splash the walls in all of its pea green-colored glory on the big movie screen, which is why I’m gleefully counting down the days to watch this 1973 classic in all its glory in February, thanks to the fine folks at Joplin’s Bookhouse Cinema.
So, in the passage in the question, it's describing somebody violently ill who is:
… pitching black ropes of [sick or vomit] over the side …