I'm a mathematician who has studied voting systems and this same weird claim appears in every US election, but only on one side.
No, it is not the case that voting third party is voting for Trump. Try it out with poker chips or something.
You might just as well say that a vote for a third party is a vote for Biden!
In fact, at any time about 90% of Americans live in non-swing states - states where their votes are mathematically almost worthless. In those non-swing states only, mathematically your best power for your vote is to vote for the third party most likely to win something. Of course, in a swing state the best power for your vote is voting for one of the two major parties.
You can mathematically prove every statement I've made, but they are simply common sense. Who could possibly believe the statement, "A vote for Manchin is a vote for Trump", if they thought about it for even two seconds, or tried it out on a piece of paper?
A lot of the reason that America is so close to losing everything is precisely because there are no third parties. The Republicans offer things to appeal to the far-right; the Democrats offer things to appear to moderate Republicans; no one else gets much of anything.
I moved to America in 1984, and it looked at the time as if socialized medicine was coming soon. I left in 2016, and now no one even mentions it.
Two pro-war, pro-Wall Street, pro-fossil fuel, anti-socialized medicine parties. Yes, one of them is full of dangerously crazy people, and the other isn't, but there won't ever be progress this way.
And now the US is at the point where any election might spell catastrophe, and people are still spreading ridiculous falsehoods about how US elections go.