After the first arrival of the wolves on the island, they actually saved the moose population, as well as the vegetation on the island, even though that may sound absurd.
The moose population was so high that they were right on the edge to rich a number that is not sustainable. That would have caused overgrazing and destruction of the vegetation on the island. Once there was not going to be more food, the moose population would have starved to death.
The wolves arrived on the island just on time. They started to hunt the moose, mostly the old ones and the youngsters, thus decreasing their numbers, but also slowing their reproduction. The number of the wolves was not growing too much because the territory and the food source for them was limited. That led to stabilization and balance in the ecosystem.