I'm no expert, 'tis true. I understand from the reading I have done that it was not the subject matter that determined a chantey, but the rhythm. There is documentation of sailors adapting shore-side songs for shipboard labor ("Billy Boy" and "The Little Ball of Yarn" come to mind). The rhythm of "Final Trawl" would fit long-haul halyard work well, based on my experience. It is likely that, because the song was written in the late 20th century, it's never been used as a chantey.
You have raised an interesting question: did sailors on wind-powered fishing vessels use chanteys?