Well, actually we can't say, as it applies to this eel, because we don't actually have a fossil of the basal group yet. We hypothesize that it retains many primitive traits common to the first eels.
Understand that homologies persist for a very long time, so those characters that are discussed in the paper are those that are inferred to have been features of the earliest eels. On the other hand, analogous characters are quite flexible, and so the eel might appear to be very different than ancient members of its group. Or it might not; the fact that this relict population was found in an environment that has remained constant for hundreds of millions of years, suggests that it might be much closer to those ur-eels than it would otherwise be, due to stabilizing selection.
Picture a bat, a mole, an ape, and a horse. Each has highly modified limbs that appear to be quite different. They are homologous, because they can be anatomically and genetically shown to be derived from the same structures of a common ancestor.
On the other hand, look at a shark and a dolphin. They are superficially quite similar, but their structures are shown to be genetically and anatomically quite different and not from a common ancestor. They are analogous.
The thing that trips people up, is that analogies are more obvious than the deeper homologies.
Does that help?
Right. It's really important to taxonomists, and occasionally has an application in medicine or in agronomy or animal husbandry. Otherwise, not so much for the average person. But the big whoop about this was that the new eel has the predicted homologies for the basal group of eels. Picture the party going on in the break rooms of ichthyology departments worldwide.
You and I, not so much.
