The piece that is new is showing that only equal amplitude observers can be thought of as "equivalent" for their definition of equivalent. Previously, one "obvious" thing to try to do was to weight different "worlds" equally, and this answers that objection.

But also important, its actually pretty clear. A lot of quantum foundations papers are rather poor, its nice to see a contribution thats well reasoned.

Edit to add: Just because I think its interesting and clear doesn't mean its correct. In particular, by neglecting the small off diagonal terms in the density matrix they are doing exactly what Everett did in his original derivation, which is only valid in the limit of infinite interactions.