Such a poorly researched article. The author doesn't know much about Russian or Ukrainian culture or history. But spares no opportunity to throw in the word 'Ukrainian'.
Gogol's letters to his parents, relatives and friends are published and well-known, you can go and read them here:
http://gogol-lit.ru/gogol/pisma-gogolya/index.htm
They are written in perfectly understandable if slightly archaic Russian. Zero Ukrainian influence can be seen, unlike in his Dikanka/Mirgorod collection of short stories. This makes me think that Gogol wasn't 100% fluent in his supposedly native Malorossian dialect.
Not sure about Gogol's contemporaries, but there is almost no linguistic distance between modern Russian and Gogol's prose. The reason is simple -(in the later half of 20th century) every single Russian had to read Gogol in middle/high school.
His influence on later Russian prose was also immense. Basically, the Russian of Dostoevsky, Turgenev, Chekhov, Bulgakov, Gorky was built on foundations laid down by Gogol, with Pushkin thrown in for a good measure.
If that defines Gogol as a Ukrainian for you, you are welcome. Why not call him a Polish writer then?
[To clarify: My opinion is that he was born, was citizen of and lived in Russian Empire. He was thinking and writing in Russian language. Thus he was a Russian of Polish/Ukrainian descent, not a Ukrainian.]