Long ball as being English has always been a crude caricature that misunderstood the essentials of the English game, as I've mentioned on the forum before.
High tempo, physical, and direct (read: not long) are the more traditional characteristics. High tempo, in the sense that quick transition from defence to attack was preferrred. Physical, in the sense that referees have a higher tolerance for body challenges and defenders relied more on their tackling ability than positioning or intelligence to defend (see John Terry, who was more intelligent than people give credit, and Jamie Carragher). This also tied into the preference for big and strong players, which has negatively affected the development of technical players in the English game. Direct, as mentioned previously a lack of back passing - even now if teams pass back to their defenders they'll elicit groans and/or boos.
These characteristics can be difficult to play against if you aren't a high-quality team - it's why we traditionally struggled in Europe as we were playing the best of the continent. In the early stages though, we'd make mince-meat of teams without the technical proficiency to deal with it.
Trinidad wouldn't do well under such a system for long, and I don't think it would characterise Fenwick's tactics. From the games I've watched in T&T, the tempo is significantly slower than the English game and there's a greater emphasis on individual skill/talent to make breakthroughs. I'd say there's greater emphasis on attacking down the flanks (ironically) - it's rare to get a dedicated right/left-back in T&T, they're nearly always a converted winger, and very few converted Centre-backs (like in England) and this produces its own unique balance on the wings. Wingers also seem likely to be frustrated strikers, and vice-versa - there's a fine line between the roles for a significant number of attackers. Out-and-out strikers like Willis Plaza aren't as common as in England, as physical players who can head a good cross seem devalued in Trinidad (but forgive my ignorance as I'm not so sure on this point as my others). Relatedly, Wingers nearly always seem to be inverted or inside forwards, who's primary aim is to beat their opposite number rather than put a cross in.
A lot of this might be out-dated given the paucity of local games lately...
There are, however, similarities between T&T and the lower-leagues - the types of play wouldn't be out-of-place in League Two or the Conference National. The Super League, from what little I've seen, has similarities with Conference North/South - some tactical awareness, but mostly characterised by the two or three players who have some special characteristic, be it flair, vision, speed or finishing.