Yes, the segregated state is the easily-reached equilibrium (you can tell it's an equilibrium because people stop moving). And, to be clear, it's an equilibrium because people have actually stopped moving -- you could imagine a dynamic state of constant move where at any given time it's still very segregated.
And indeed, that is what the data paper that the article links at the bottom (http://smg.media.mit.edu/library/Clark.ResidentialSegregatio...) suggests is true: Because in the real world, diversity preferences are not symmetric. That is, "triangles" may want to live with 3+ other "triangles" around them, but "squares" don't also want 3+ other "squares," they want, say, 1+, or indeed they want 3+ "triangles." That prevents the static equilibrium that the simpler model predicts, and means that people keep moving. The dynamic "everyone's always moving" may still be segregated, but the point is, it does not have the same property that the article highlights of "everyone moved to a state they can live with, and now even if they would be comfortable with a more diverse neighborhood, nobody's moving and so no diverse neighborhood ever happens." Because they are still moving.
I don't have the expertise necessary to critique the data collection or manipulation of that paper, so perhaps it's wrong, but I'm taking it as provisionally true that they are correct that no equilibrium exists.