Just to make it clear, when I talk about the rule of the law, I'm talking about the formalist interpretation of what that means. Which requires the law to be prospective, well-known, and have characteristics of generality, equality, and certainty.
The Athenian system lacked at the very least the aspects of:
- prospective: there were no set of rules for the future, as such. Except, duly noted, for how juries should work. But other than that, is there anything saying you're not doing anything wrong by speaking in favour of peace with Sparta? Or even by being the prosecutor in a trial? No, there was no such thing. Even starting a trial within the legal framework could get you then tried for it and executed, as those who accused those admirals discovered the hard way.
For most practical purpose, their law was fundamentally retroactive. They sought to decide if what had been done was ok to do, rather than tell you whether it's ok to do something in the future.
- well known: there were no rules for anyone to know, other than how juries should work. It could not be well known whether you must risk more ships to rescue survivors in a storm, and in fact even retroactively they flipped between it being wrong and being right. Pretty much whatever you contemplated doing, there was no way to be well known whether it's ok or not. In fact, there was nothing to know until the jury voted on that.
- certainty: ditto