If I wrote a book for beginners it would probably look a lot like Learn Chess by C.H. O'd Alexander except for two things: One I would make it easier to read and two, I would include at least a little about positional play at the end. Nothing complicated but enough that they can understand what's going on in a game even if they don't know how to apply it yet. For example, understanding the idea of mobility encapsulates a lot of positional play. Same thing with the idea of time. The specifics can come later but if the beginner can understand why he's losing then that can prevent some frustration even if he's not sure how to do it yet.
As far as your idea, I dont understand the order of some of the things you have on there. I would think the first thing you would teach somebody, after how the pieces move, is how to mate. Otherwise, they're just moving pieces around with no concept of what they're trying to accomplish. That would be like teaching someone to fire a gun by having them shoot randomly in the air. After that I would explain how to mate with 2 rooks vs. a king so that if somehow they manage to get a winning position they can get a win out of it (it is IMO the simplest mate to understand) . Losing every game because you can't mate would be very demoralizing.
Some of the endgame concepts (like the opposition) are WAY too advanced for the level you're talking about. I play 1500- 1800 rated players all the time that make mistakes with regard to the opposition or that grab that backward pawn that you talked about. They're nice concepts to know but they aren't necessary to move beyond the beginner levels. Besides if they learn to calculate correctly they can figure some of that out on their own (which is the best way to learn something because it makes it intuitive ). And again the order seems strange. When teaching each idea should build on the last but you seem to be doing the opposite. For example, why would you teach K, P vs. K BEFORE you teach K,Q vs. K. I can just see a beginner executing a flawless K,P vs. K endgame and then after Queening having to take a draw because he cant mate with a queen. Seems ridiculous to me. The way you have the endgame being taught seems almost completely backwards.
After they know how the pieces move and how to mate, I would start back at the beginning and work through each area of the game beginning with opening principles (as if walking through a game) all the time showing how those things relate to the ultimate goal of checkmate. Your chapter 2 seems too advanced for the entire book let alone the 2nd chapter. Players should learn to do things first then later figure out what they're doing. I wouldnt't bring up board vision until much later because its going to be a long time before a beginner can even think about playing without making huge blunders. Material is important and should be emphasized but beginning very simply and building slowly. First, showing that you can win material by attacking something with more pieces than the opponent has. Then the concept of the double attack (again, concepts before specifics) and only later showing specific types of double attacks like forks. Later more advanced tactics like pins can be introduced. Incidently, that's pretty much how the book I mentioned earlier presents it.
I would think the goal of a book like that would be to get the player playing and winning as quickly as possible so that they enjoy the game and will continue to want to get better. But, you don't even teach them how to win until the very last chapter and they'll have to wade through a lot of stuff thats way over their heads and that's not going to really help them even if they did understand it just to get to the part that tells them how to win.
I could go on. But if I were you and wanted to see how to do something like that, in addition to the first book I mentioned, I would look at other books like Pandolfini's, or chess for dummies or any other beginner books and see how they present things i.e. what they did right but also what they did wrong.