First, it's not "America", it's "The Americas" -- we're talking about the two continents, right? The New World?

Second, that's the word we use in English. If you've lived here for millenia, you can use the appropriate word in your own language.

You have to call it something. Place names are a function of language, not of genetics. In English it's called North America or South America, and together The Americas. In Chinese South America is "South Beautiful Continent".

Oh nooo, I'm so offended that Chinese people have a name that I didn't agree too for the place my ancestors are from for the last 350 years. Someone give me some pearls to clutch.

But that’s what it’s called in English, the language the article is written in.

Germans don’t call the place they live Germany. They don’t even call themselves Germans. But I call it Germany because that’s the English name for that place.

Their "point" was nothing more than repeating the colonialist propaganda that the real americans were the ones who ""settled"" later and named the continent.

(ALso that is a so ridiculous reasoning, by that logic everyone is native african and not native <insert place where they genetically diverged and settled>)

There are multiple usages, specifically just citizens of the USofA is just one use.

American, a. and n.

(əˈmɛrɪkən)

  A adj. 

  1.a Belonging to the continent of America. Also, of or pertaining to its inhabitants. 
  1.b American language (usu. with the), (i) a language of American Indians; (ii) American English (see sense 3). Also American tongue. 

  2.a Belonging to the British colonies in North America (obs.). 
  2.b Belonging to the United States. 
  2.c U.S. spec. (See quot. a 1861.) 

   1837 Diplom. Corr. Texas (1908) I. 187 A large number of fine American horses‥which there is no doubt had been stolen from citizens of Texas.    1846 E. Bryant What I saw in Calif. (1849) iv. 37 Such [Indians] as rode ponies were desirous of swapping them for the American horses of the emigrants.    a 1861 Winthrop John Brent (1862) ii. 14 He was an American horse,—so they distinguish in California one brought from the old States.    1878 J. H. Beadle Western Wilds, xvi. 253, I rode a good-sized American horse.

  3.a Special Combinations. American bar; American blight; American cheese; American cloth; American dream; American English; American football; ...oadfoot et al. Billiards i. 41 In 1876 D. Richards‥ran second to Cook in an *American tournament.    1976 Cumberland News 3 Dec. 19/1 On Thursday, December 16‥a Christmas American tournament will take place.

  3.b In the names of various trees and plants native to North America, as American arbor vitæ, Thuja occidentalis; American ash, Fraxinus americana; American aspen (tree), Populus tremuloides; American Beauty (rose), a variety of cultivated rose; American beech (tree), Fagus grandifolia; American elm (tree), = white elm; American plane (tree), the buttonwood or Virginian Plane (see plane n.1 1). 

  B n. 

  B.1 An American Indian. 

  B.2 A native of America of European descent; esp. a citizen of the United States. Now simply, a native or inhabitant of North or South America (often with qualifying word, as Latin American, North American); a citizen of the United States. 

  B.3 A ship belonging to America. 

  B.4 pl. Short for American stocks or shares. 

  B.5 American English; the form of English spoken in the United States.

Yes, that is one use of the demonym “American” in a modern, geopolitical context. There are other contexts and other uses when it has different meanings.

Asserting it has that meaning when used in context of a time tens of thousands of years ago is nonsensical.

I suspect "enlightenment" is that the inverse is also true, but I think that this concept, as most are, is not reversible. In the animal kingdom, invasive species are often a detriment to the local species. In the human world, incoming cultures are often a detriment/disruption to local cultures. This is especially true when the incoming culture has an incompatible value system. For example, see the many examples of Islam and Christianity decimating/erasing local cultures, over the centuries. The value system can be so out of whack that you end up with genocide of the native populations, like in Canada, USA, and Australia. The tricky part is that the very perception of "disruption" depends on if a culture is valued or not, with many modern cultures have little/no accepted value. Related, this is why religious cultures are the most disruptive: religion is culture that's strictly defined in a personal way, with high personal value, so high rigigity. Rigid things don't mesh well.