Director Kirby Adkins says his greatest fear about “Mosley,” his ambitious animated feature about fantasy creatures called thoriphants, was that too many compromises would have to get made along the way — and that the movie would become “screwed up.”

Making “Mosley” as an international production — it is the first film to make use of the bilateral New Zealand-China treaty — and delivering a nuanced, family story that goes beyond purely kids’ entertainment, both seem to add to the risks.

Previously called “Beast of Burden,” the film follows the eponymous hero Mosley and his family of intelligent four-legged creatures who have the ability to speak like humans but who have been cursed to live a life of servitude. In an attempt to free his family, Mosley embarks on a perilous journey to find the mythical land of Kinesareth.

That it avoided most pitfalls and has now begun its theatrical career, kicking off through Rialto in New Zealand,...