So the map is actually pretty accurate and it really illustrates the nature of the "Island Hopping" strategy employed in the South and Central Pacific.

If a location was not needed for Allied basing purposes it was avoided. But it was also then generally pounded to dust by air strikes as well. For example we can look at Truk and Operation Hailstone in February of 1944.

Truk was the IJN's primary forward base in the Pacific, describe as Japan's Pearl Harbor. And as opposed to invading the well defended island, from which most fleet units had already been withdrawn the USN instead decided to neuter the base and select another location for a base. Thus for two days the carrier force rained hell on the island and its sizeable garrison, destroying virtually all ships they found in harbor, along with the vast majority of the island's air power. And even at one point Rear Admiral Willis "Ching" Lee took his surface forces, including the battleships Iowa and New Jersey in to engage fleeing Japanese shipping.

A similar raid had occurred over Rabaul in November of 1943 where a Japanese cruiser force threatening allied landings had been savaged along with the crucial Japanese base being badly roughed up as part of the war of attrition in the Solomons.

And while the islands marked in red did generally still fall under the control of Japan, it would be better to think that anything beyond the beach into the sea was firmly in Allied hands. Japan had very little ability to supply her remaining possessions, or even reinforce or evacuate garrisons. What ships remained afloat were in large part immobilized for lack of fuel or unrepaired damage. Leading to steadily worsening supply situations on the isolated outposts, to the extent that starvation was a real threat and more than once the forces resorted to cannibalism.