Weird you read socialist news.
It's a bit bollocks though because the only ballots that a political party can control are primary ballots... and those are for voters to pick who will represent that party. So yeah, you wouldn't see third parties on that - because that's not what the point of those ballots are. Those are for parties to pick their candidates.
For the general election, each state sets the rules for what lets you get on the ballot - not any party.
So it's just some made up bullshit to try to equate America to Russia to convince the lowest information US voters and foreigners who have a weird obsession with US politics but refuse to have any real sort of understanding about US politics.