What I mean is that formally, those laws (Sharia) are not applied selectively. The practice is different, but that's not quite the same thing. Historically, when the concept of rule of law was first introduced, it was to counter the then-prevailing idea that laws officially don't apply to kings, who are above the law. In places like Russia, this was even manifested as part of the title - "autokrator" grew to specifically mean that the ruler is not subject to anyone else's will (including any laws).

How does that differ from this: https://en.wikipedia.org/wiki/Sovereign_immunity_in_the_Unit... ?

You can still sue any specific person, just not the office they represent. E.g. if the Senate passes a law, all senators are still subject to that law as individuals.

The other side to rule of law is that the government can't punish you arbitrarily - they need to have an applicable law, and they can only apply it to you as written (including penalties etc). In a system without rule of law, a subject can be charged with wrongdoing on the whim of the ruler. That part is also missing in KSA.