The writer of the article said something like "white people determined who was and who wasn't a n-gger in a way that both helped them and hurt Black Americans."
Is it true that race only exists because of racism?
Would you mind citing your source? The statement that "racism created race" is a bit vague and prone to multiple interpretations.
A better way of stating it would be that the idea of race was reinforced by the ideological need to differentiate between economic classes, when other political ideas of the time said that persons are equal in rights and liberties. The development of modern ideas of race, at least in the United States, must be understood against the backdrop of a social tension between the need of the large landowners of the new World for cheap disposable labor, and the political philosophy of the time that suggested that "all men are created equal". The easiest way to resolve this contradiction is to says that some humans are not "men" in the sense that they are social beings of equal rights with other humans. A useful comparison may be drawn with Russia, where large landowners had a need for cheap labor, and so created a social system that held the workers to the land, but did not go so far to suggest that the workers were less than human, since the prevailing political ideology did not require that all humans (or at least adult male humans) are equal in rights and liberties.
This would be a better question for sociologists.
Though it's not a direct answer to your question, we did get an incredible answer to a similar question on the development of the idea of races. You can read it here.