Good question. I'd say that the ties back to imperialist days on Earth are there because (1) it's a popular idea to hate this part of history, and (2) despite having lead characters who are asian and black, the show is still implied to be "white enough" for the comparison to be justified.
The claim is that Star Trek's premise is a problem because it makes the flawed assumption that one culture can be better than another, and by extension, that all cultures must be valued and respected equally. Without going into the cultures of humanity in Star Trek versus the Klingons, you can examine similar claims closer to home even where some cultures are deeply invested in medieval-level cruelty like stoning of homosexuals and adulterers, female genital mutilation, and inhumane punishment by knife and cane. But these realities don't fit the author's narrative, and therefore must be ignored for the purposes of the thesis. Like Klingons, they're a benign minority who are simply misunderstood by their would-be cultural oppressors.
The article's ostensibility about science-fiction, and managed to stay on point for the first couple paragraphs, but it quickly devolved into the author's pet theories on race and gender. I really had trouble with these sorts of broad and totally unfair generalizations:
> Uhuru was a service worker and Worf was a punching bag; when the show made a black captain, was it a coincidence that the show also became “darker” and less optimistic, when its characters started to be “flawed” and “ambiguous”? Voyager had a female captain, but it marooned her to the farthest reaches of the galaxy (and the less said about the garbage politics of the reboot movies, the better).