The calypso competitions on other islands are I believe a recent (post 1950s) innovation, inspired by Trinidadian carnival. E.g. many mento performers in Jamaica began calling themselves calypsonians after Kitchener's visit in the late 1940s.

In the period discussed here, I think it is perfectly valid to distinguish between Trinidadian calypso and the musical forms of other islands; indeed I think it is ignorant not to do so.

However, my main reason for not considering 'Jamaica Farewell' a calypso is that (in my opinion) it is musically not a calypso. The melody in particular is unlike any Trinidadian calypso that I can think of (although I am happy to be proved wrong).