I have gotten the exact opposite impression. Maybe 25+ years ago when many Westerns on the hard left naively celebrated communism and the Soviet Union, but the only people who seem to sympathize with Russia are those on the alt-right who wish that the POTUS had the chutzpah of Putin when dealing with foreign adversaries.
The irony of using "alt-right" in this discussion is also delicious, considering it's turned into a pit for people to be thrown into by the media rather than a label for those who adopted it.
It would be fair if the source of the allegations wasn't likewise tainted.
Russia engages in propaganda, and this is abundantly obvious; it would be nice if those claiming such were forward and honest about their own ethical deviancies and the actions of their own state. It is tiresome to hear but one side of the concern from the media.
As Chomsky says, propaganda is to a democracy what the bludgeon is to a totalitarian state. The NYT is very much an American pro-establishment paper staffed by upper middle class ivy league graduates. If the NYT isn't intentionally slanting the news in its favor, then it is merely reflecting the slant that is rather uniform among its journalists and editors.