Neither is 'real'. The power of might depends on belief just as much as the power of rules. You need a whole lot of compliance, even when forced by fear and terror, to just keep up a police state. The belief consists of where people think other people assign authority to, at large. But that can be just as brittle as a meme stock if the time is right.
Social reality is always constructed. No single construction is more real than any other.
"rules-based order to might-makes-right"
These are the same. They are the same because someone has to enforce the rules. The reason why this entire discussion is so obtuse is because you refuse to accept this. If I was wrong and they were different, you wouldn't treat the US and others (say China) by the different moral standards. To bring this back to an individual level, this is the same as saying police don't deter crime. You wish these two concepts were different so you let your political bias blind you to reality. That doesn't effect reality though. Police do deter crime and whoever (the US) enforces the rules based order has to do so (from time to time) kinetically.
A system that is closer to physical, tangible reality is more "real" than one built on many layers of concepts, beliefs and ideas.
Just as "real assets" like buildings, machinery and metals are more "real" than abstract assets.
Abstract assets like shares of a corporation, intellectual property, cash in a bank account, promises to deliver a commodity in the future, and other intangible concepts only exist because we collectively believe they exist and trust each other to follow rules.
There are real weapons and prisons at the bottom of this stack of abstractions to force people to comply, but it's mostly collective belief, trust, culture and tradition.
When we devolve from a rules-based order to might-makes-right, those layers of abstraction between us and the weapons evaporate, and ordinary people like moms and ER nurses get gunned down in broad daylight by agents of the state asserting raw power.
Abstractions like law and due process evaporate, and the "real world" underneath is nasty, brutish and short.