From A.L.Lloyd & Sea Chanties –

Me/Gibb: >>Neither did the sailors on the Gazela call them "shanties." Their 2400+ year histories and traditions are not about African-Americans, cotton screwers or the Gulf of Mexico.<<

What do "them" and "their" refer to?

Them: The rhythmic sounds that any sailors made when going about tasks in unison.

Typical:
“PORTUGUESE
5175. ZALOMAR, v. to sing out
SPANISH
3481. Zalomar, v. to sing out
[A Marine Pocket Dictionary of the Italian, Spanish, Portuguese and German Languages, 1799,]

“Celeuma, sf. (naut.) a seaman's cry when hoisting.
Celeumear, vn. to cry as seamen do at work.
Zalomar, va. (naut.) to sing out.”
[A Dictionary of the Portuguese Language in Two Parts, Elwes, 1884]

Their: In context, Scots and/or Portuguese. In general, +99% of all recorded history. Even for 19th century Anglo merchant marine, “anchor/capstan/windlass song” &c were more common than “chanty/shanty.”

Scope? Thomas Moore (or his editor or publisher) chose Quintilian for the Canadian Boat Song's epigram - Et remigem cantus hortatur. The Portuguese zalomar's etymology shares the same roots.