The reason for this is simple: the word in English is “American”. Because in English speaking countries, it is almost universally the case that we talk about the 7 continents. And in the rare case we talk about 6 continents, it’s from merging Europe and Asia (which, frankly, is blatantly a far superior model of the continents), not merging North America and South America.
So “America” unambiguously refers to the country, and there’s no need for estadounidense, any more than there’s a need for “commonwealthian” for someone from the Commonwealth of Australia.
That sounds like the name of a person from Docklands in Melbourne.