The rule of law and the basic functioning of the state is one and the same. The state sets and enforces the law. The state's strength and the consent/will of the populace determines the success of the state and the law.
The states in the Arabian peninsula have strong legal systems, yet they are highly inconsistent when it comes to serving the people. For example, Saudi Arabia has very strong legal enforcement, but you wouldn't want to be black or a woman there.
But "rule of law" is not really the way to describe them, despite "strong legal systems".