Well, given that the culture of Old Ghis was trodden into the dirt thousands of years ago, it’s probably something of an invented tradition. Especially since the word “arch” or “archon” is Valyrian, not Ghiscari, in origin.
My guess is that, following the fall of Valyria, the remaining cities that had once been part of the Ghiscari orbit (Astapor, Yunkai, Meereen, New Ghis, Elyria) were each ruled over by an Archon in a league of eight. The other three were probably Vaes Mejhah, Vaes Diaf, and Vaes Efe, three Ghiscari settlements that the Dothraki sacked during the Century of Blood.