it implies theres an order to the world and universe, and theres some sort of supernatural power in control of determining which actions and thoughts are just.
No, a higher power is not necessary for karma.
I see it as an equilibrium of the actions of the universe, a very complex balanced system. Nothing to do with whether the actions are 'just', IE: You do something good or bad that has an affect on someone or something else, which in turn affects something else and something else either positively or negatively until it comes back to you...sort of like a cycle. If the action was neither positive nor negative, neutral, than it's affect on others and in turn back to yourself in the future will not be significant.

It's also a bit of common since on a basic level example: Play with fire, you're going to get burned. Stick your finger into a light-bulb socket, you'll get electrocuted.

I don't believe in order, I don't believe in chaos...I believe in chaotic order.
What the fuck is chaotic order?
The universe my all be random, but in the end it all works out.