Maybe he hopes to replace one of the existing parties (that is, become one of the two dominant ones).

No, their strategy is to focus on reform from the bottom up: getting local officials elected at the city, county, and state levels in order to pass electoral reform (states control election in the US) to make our national politics less inflammatory. Parties matter less at these levels. Their main goal right now is to get ranked choice voting passed in as many states as possible (focusing their energy on ballot initiatives). They are also not a "party" (they are registered as a PAC). This way, republicans or democrats can receive a foward party nomination without having to leave their own parties and run independent. They just have to be aligned with forward party goals. They have maybe 1 or 2 US representatives that they're tracking, but Andrew Yang is not running for president in 2024 because it would just be a waste of money to them. The vast majority of their advocacy is at the state and city level

Sure, that's always the hope. But leaders in two existing dominant political parties have gotten pretty good at triangulation. As soon as a nascent third party starts gaining significant support, the existing parties co-opt pieces of that platform and the third party fades away. So, third parties can be temporarily effective in moving the political needle but they won't win major elections in our lifetimes.

Breaking that is the entire point of ranked choice voting. If the existing parties co-opt that, then the party has succeeded.

I'd suggest you read all the way through your linked article, including the subsection "Counterexamples".

I agree: starting a third party with our current electoral system seems both counterproductive (because vote-splitting hurts the interests of its supporters) and short-sighted.

This wouldn't be the case if we used a system like instant-runoff voting ( see https://fairvote.org/ ; https://www.americanprogress.org/article/its-time-to-talk-ab... ); I hope the people who are interested in parties like Forward will also get behind those kinds of reform.

Electoral reform is actually one of the biggest issues that the party seems to back. (For exactly the reason you mention.)