Kiwi here. They live in alpine regions, they have adapted to alpine life - how are they not alpine parrots? Go back far enough and you could make this argument about anything.
Sure man, if 700 years is far enough for you. Meanwhile, human spent thousands of years to domesticate junglefowl into chicken.
Domestication ≠ habitat classification.
Alpine refers to habitat. Kea live, feed, and breed in alpine environments and are behaviourally adapted to it.
By your logic, because my ancestors ~300 years ago aren’t from New Zealand, I’m not a New Zealander.
Sure man, ask the Keas, I am sure they like their new name and wouldn't prefer to live in lowland if human were to disappear in NZ.