… I know we’re supposed to “keep playing until a clear winner emerges” but shouldn’t that be just between the two players who tied?

A: Actually, when the rules say to “keep playing until a clear winner emerges,” that does mean “until a clear winner emerges among ALL the players”. So, in your example, the third player absolutely wins.

Sometimes there’s a tie, and what happens is that the tie is eliminated when the Goal goes away, and the game just continues until someone wins in a totally different way. That’s probably the most frequent way that “tied” situations are broken by continued play, actually.