The Rambam does not put any form of government in the category of natural law. I assume he had read Aristotle's/ book on the constitutions of the Greek states.
He puts the nomoi of the Greeks and ravings of the Sabians all into one category. Clearly to him only the Torah itself can guarantee natural law.
This leaves one wondering nowadays when one finds religious neighbors to be particularly obnoxious, what could the Rambam have answered? That they are not keeping Torah well enough? Then what kind of state did he envision? One in which everyone is a tzadik?It is well known living under the rule of religious authorities is a Kafkaian nightmare.