I'd just like to note that the "Gov of Men not Laws" was a relative latecomer in OTU canon.

In CT there were a number of references to nobles that only had a 'titular' role similar to the various crowned heads of europe.

Now, in that case, I guess the 'men' would be whomever does have the power to dictate. 

Prime Minister, etc.

That does not alter the fact that the imperium is ruled by a hereditary noble class, *without* a central body of law and justice system that they are subject to other than the authority of their superiors.

That SOME nobles have ceremonial titles in this context is meaningless (especially since the Imperium allegedly does not directly rule the worlds) ; there are also numerous references to ‘working noble titles’, noble rank granted on a non-hereditary basis to people holding particular offices or charged with a a particular task. This means that there is a hierarchy of authority that is attached to the nobility. 

That’s the definition of ‘rule of man, not law’.

On the ground on the various planets you can have the full gamut of government types, but those don’t apply beyond 100 diameters, so practically speaking probably 99.999% of the sophonts in the Imperium DO live under some form of rule of law, because that’s all local. 

The Emperor rules the space between the worlds by edict, and has the full force of the Imperial Navy Army, Scouts, etc who declare personal allegiance *to him* to enforce those edicts.The Nobles who interact with those worlds derive their authority from the Emperor, not any body of law.