After reading through it, I did not see anywhere that a realm applying for an Elder seat must technically be a theocracy. All that was listed were requirements that were deemed "theocratic." In short, this is all semantics, no? Am I missing something, or is this entire argument over some ruffled feathers?
To support this observation, Classically, OOC, theocratic realms are where the priest double as the ruling class. That would mean ever regional lord, duke, and ruler, must be of the priest class. While I personally think that this would be a supremely interesting development, it is not in the game mechanics and is thus a moot point. As I understand it, no single realm in SA follows this model.
One would call a realm that governs itself by theocratic principles is, a theocracy.