I cover this in Dave Arneson's True Genius; and NO, I'm not trying to sell you the book!

But it is covered in full therein. VERY BRIEFLY (consider this a toyish abstract): What we do in RPGs is mostly self-organized imagination, constantly changing except when we need "mechanics" to adjudicate outcomes. Thus Arneson's systems architecture is an interdependent fusing of Conceptual and Mechanical systems, a super system which has no historical antecedent that I have found (to date).
What Rob is describing can also be compared to computer programming.
The Game Engine, or Play Method is the core of this system.
So lets pretend the Game Engine is a computer program and that you are using an object oriented computer language.
You have a Main program module that begins the program.
1. Since we are actually using language as our Programming Language when we play, we are relying on semantics in order to establish what the Game Engine is doing.
2. Also, consider that in a Computer Program one must have error handling. Error Handling is a way to keep a program from Crashing/failing because data that is entered does not match any expected input type.
So when a DM says something as simple as: You walk down a hall and come to a door. This is your Main Program establishing a set of parameters for the situation at hand.
The game engine is the verbal exchange that we use to enter within this play method and is the Role Playing.
In a computer program one is limited to very specific input as a user. Yet with the RPG method, everything is flexible. That is the power of it.
So back to Error Handling. With a Computer if it says Enter: Y/N , if you enter anything else the program has to be able to parse whether you did Y, or N. But what if you enter a number, or symbol? Without error handling the program will crash.
Because Arneson's Game Engine is using language, it is possible to do something different.
Common responses to finding a door are : I listen at the door, I open the door. With Arneson's game you can expand the terms. Lets say a player asks: what is the door made of? The Referee Says: wood.
Now our semantic premise has changed to: You walk down a hall and come to a door it is made of wood.
This is a recursive function within the Arneson Game Engine that comes about because of how flexible it is. A recursion is best described using the Fibonacci sequence. 0 + 1 = 1, 1 + 1 = 2, 1 + 2 = 3. 2 + 3 - 5, etc.
You are using previous data to create new data and growing and expanding what you have as a result.
So long as you are using language to run your game, you don't need any rules.
Object oriented languages use what are called, calls or methods, which are basically rules. If a user inputs something that matches the need for a call, a new program is briefly launched in order to generate a result of some kind. Thus if a player says: I open the door. A call is made for a specific rule. In this case it is the written rule for opening doors. Now we are implementing a rule.
The rule for opening doors is a binary Yes/No result. As a computer program, one would generate a number from 1 to 6 and then if the number was a 1 or 2, the door is open. If the number is 3 to 6 the door is not open. The binary value of Open/Not Open is then returned to the main Game Engine.
Lets say we get a Door Opens value. The Rule has been used, we know a result.
Within the Game Engine our premise is now changed to: You walk down a hall and come to a door it is made of wood the door is open.
What Rob describes in his book is the first time someone has assessed and described this kind of operation within an RPG. His understanding that we have two things: a Game Engine and Rules is a profound conclusion.
Most gamers do not understand what they are doing when they play. They do not understand that the simple little
Example of Play is actually the rules for how to use the Game Engine. And that when you use rules, those are entirely separate from the Game Engine and are merely a way of introducing fairness and randomization to what happens when we play the game.
The Game Engine is what Arneson invented. And as Rob has pointed out, you can't play any RPG's without this flexible and simple play method.