Answer

The Ran’s novel position is a lone view which, as I understand it, has no source and not much logic either. The authority of an ordinary Jewish king is also derived from "the law of the kingdom is law." So I would not be concerned about that.
But in any case, it makes no practical difference, since the institutions of the state and its laws have validity by virtue of communal enactments, even if "the law of the kingdom is law" does not apply here.