Kong isn't just eating food from the island, he's also gathering sustenance from the sea.
A squid partially emerged from the water. This was a true giant, far
larger than any Chapman had ever seen or even heard of before, perhaps
eighty feet from tip of tentacles to the end of its tail. It was a
powerful creature. Several limbs remained hooked onto something
beneath the surface as the ape tugged and wrestled to haul it out.
Water churned in the violent struggle, turning dark as the squid
released sprays of thick black ink that spattered down around and over
Chapman. It stank, a heavy viscous fluid that stuck to his clothes as
thick as tar.
Chapman curled against the rock and waited for it to all go away. He was moaning softly, listening to the sounds of the giant ape eating. The tentacle end lying across his legs went limp, then was jerked away as the beast finished its meal.
Kong: Skull Island - Official Novelisation
There's plenty of food in the ocean, enough to feed an entire army of giant apes.
Additionally, as has been pointed out in comments, the island itself acts as an entry-point into an entire hollow-world ecosystem of giant monsters living under the Earth's surface.
Their hypothesis is proven correct but quickly draws the attention of
Kong – which was the real motive behind the bombing of the island. The
giant gorilla makes swift work of the helicopters that the scientists
and their escort arrive in. Once they’re stranded in various parts of
the isle, the scientific team and the soldiers work their way around
the forests and jungles, encountering giant spiders, pterodactyl-like
birds and massive water beasts – seeing first-hand the kind of life
that exists around a hollow earth waypoint.
Screenrant: Skull Island: King Kong’s Backstory Explained