Regency here really seems to be a joke off of the Hyatt hotels. But people are pretty correct, explaining regent as a non-royal placeholder (benchwarmer) to rule while the *actual* royal is unavailable. Historically, this was to give time for the true king to come of age. I'm thinking of FF Tactics on PS, way back when, where the whole war was between two nobles fighting a war over who would get to be regent for the child king. This however would not come up as units (aside from livestock...) don't age turn-wise, they just pop in maturity. Therefore, the Regent could stand in for that 60 turns for an heir to pop, should one be in the works when the overlord croaks. Or, say, there is another royal who is not the heir for some reason, who then pops the heir while the Regent rules for those 60 turns again. Either way, a temporary thing and there's no indication that the Hyatt Regency isn't in the middle of just that.
Another good example is in LOTR, the steward of Gondor is similar to a regent. If you remember the movie, he had to sit in the little clerk chair at the bottom of the steps leading up to the *good* chair (a pretty good visual scene), but by all rights he was the ruler. He even resisted when the actual king did show up. Hilarity ensued. Again, I don't necessarily see this coming up in Erfworld, excepting the case of Jillian and Faq. Jillian totally went Aragorn, wandering around distant lands ronin-style, before making her way back for a triumphant return. But it was just a free capital site, not some steward/regent there, being acting-overlord and preserving her lands in any way. But maybe the Hyatians would have set up something like that, a temporary Regent who was holding overlordship while the ruler was a field and died.