What’s really cool about this is that cephalopod (octopus, squid, etc.) intelligence evolved completely separately from intelligence in tetrapods (which includes primates, dolphins, crows… basically any other intelligent animals you can think of). Cephalopods are very, very far away from us on the tree of life. For context, you and a starfish are more closely related than you and an octopus. The last common ancestor of humans and cephalopods was the so-called Urbilaterian, the hypothetical first animal with a left-right symmetric body. This animal almost certainly had, at most, an extremely simple nervous system, without anything resembling a brain.
All this is to say that the fact that this octopus appears to be dreaming means one of two things. Either
a) dreaming is a very, very old thing indeed, going directly back to the Urbilaterian. This would mean that almost every animal, from insects to starfish to sea slugs to newts, is likely to have the ability to dream in some capacity or another (unless they have specifically lost it by evolutionary simplification).
b) dreaming evolved entirely independently in cephalopods when they developed greater intelligence. This would suggest, at least, that there’s something very fundamental about dreaming related to intelligence itself, which causes it to emerge independently when sufficient intelligence arises.
Needless to say, either of these outcomes would be really very cool.