This is because when the losing fuedal-fascist White Army fled to the island, the imperial fascist British and Americans interceded to protect their imperial fascist interests by ensuring that the KMT was able to stay alive and that they would be further indebted to them. The KMT then proceeded to prosecute the ruthlessly brutal White Terror on the island while the North Atlantic imperial fascists maintained diplomatic and military relationships with the island as a way of holding on to their imperialist presence in China that they obtained through violence, occupation, and the forced selling of opium.

Specifically that it is not administered by this particular central government of the mainland is irrelevant. The former central governments all administered Taiwan prior to the civil war, but this particular central government was stopped by European interventionism to advance European interests.