“Perhaps one innovation is that western law codes create impersonal associations with legal rights and obligations that are independent of individuals or government offices, e.g. the corporation. These enable greater collective action to compete.”
That’s what is meant by the “rule of law” - that it applies to everyone equally, including the “monarch”.
Definition:
Rule of Law - “The doctrine that no individual is above the law and that everyone must answer to it.”
There is another very important ingredient that may or may not be by default part of the “rule of law”. And that’s the right to private property and its protection by the law.
“that it applies to everyone equally,” is not a property of the rule of law throughout most of Western civilization during most of the time 1500 CE onwards.
During that time most countries were ruled by nobility and there was a distinct class structure with serfs at the bottom and kings at the top. In central Europe, monarchs often delegated to running of courts to lesser nobility, for example.