La Gomera is mostly national park so riding off road is pretty much out of the question there. You’re not getting mixed up with El Hierro are you? One of the guys from the North of Tenerife moved over there to continue his guiding.
EDIT: Just seen the FB page of the guy. He moved from FreeMotion in Gran Canaria according to his page. Still not sure how he’s getting away with guiding MTB in a national park though. That’s something they are all pretty hot on and the fines if you get caught are pretty steep!
The Canaries as a whole have the same laws, but each island seems to decide whether to enforce them or not. Even districts of islands have slightly different views. It’s a pain in the ass, and the reason we have less trails available in North Tenerife than in the South.
Gran Canaria have just recently stuck up a load of No Biking signs, La Palma seem to be embracing MTB, El Hierro too. Tenerife is currently undertaking a review of cycling as a whole, in MTB terms the proposal is to fully legalise shared use senderos (paths less than 2m wide) to bring them in line with areas in the mainland (Zona Zero for example). Only time will tell.
The Canary Islands are always 5 or 6 years behind the rest of the world!