Here's a bit more of the text to which Dúgorin is referring to, I think. On my copy, it's on page 193, within "The Northern Line of Arnor: the Isildurioni [!], and underneath the entry for the 10th King of Arnor, Earendur (The bracketed material is in the presented text, representing a strike-through that Tolkien made himself.):
After Earendur the Northern Kingdom of Arnor was broken up. The sons of the king established smaller independent kingdoms. The direct line of the eldest son ruled the realm of Arthedain in the North-west; their city was Fornost. Annuminas became deserted owing to the dwindling of the people. The chief of the lesser realms were [Cardolan east of the Baranduin; and Rhudaur north of the Bruinen. Arthedain still claimed the overlordship, but this was disputed. >] Cardolan south of the Great Road and east of the Baranduin; and Rhudaur north of the Great Road between the Weather Hills and the Bruinen.
I agree the wording doesn't make sense given that there's no other hint of successor-states to Arnor besides Arthedain, Cardolan, and Rhudaur. But more to the point, Arthedain is everywhere else presented, if not as the chief of the three, than certainly not the underling of Cardolan and Rhudaur!
Personally, given that the writing is a little disjointed anyway, I'd guess it's either a mistake by JRRT, or a corruption in the text we've been given by CT, or by his editors. Or possibly it was a passing thought by Tolkien that was dismissed or forgotten. But I'd lay a nickel on it being a mistake.
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As an aside, I can't help but be reminded of Tolkien's line in
Unfinished Tales, "The Istari":
"Of this Order, the number is unknown, but of those that came to the North of Middle-Earth, where there was most hope (because of the remnant of the Dúnedain and of the Eldar who abode there), the chiefs were five."