- Has the theory changed since Advanced Backgammon came out?
Yes, absolutely. Computers are able to get the right answer the vast majority of the time just on analysis, and on top of that they can perform rollouts of a few thousand games in a matter of hours. It would have taken players days or weeks to roll out positions in the 80s. No one has that kind of time. I made an estimate that about 40% of the solutions in Advanced Backgammon were in error. Still sounds about right.
- Has the method of approaching/analyzing positions changed?
Obviously since a lot of the theory has changed, many of the answers which are built from the theory have changed. But the general method of analysis is more or less the same now as it was then. The selection of positions, identification of key features, and weighing of key features is great; phenomenal if you consider it came out in 1984. Robertie was well ahead of his time.
I don't think any book is really necessary these days. There is a plethora of information online and the bots are good enough to get anyone to play at a WC level by themselves.
Everyone learns differently.
I started out in BG by reading Magriel and after that Advanced Backgammon. That was 3 years ago when I didn't have the first clue as to how to move the checkers and couldn't remember what the doubling cube meant. Today I wouldn't consider myself a dog to anyone in the world; Nack, Sander, whomever. Of course I owe the vast majority of that to playing against GNU; but Advanced Backgammon was one of the key works that shaped my thinking. My perspective on the game would have been a lot different if I hadn't read it.
In hindsight, did Advanced Backgammon help structure my thinking into the player that I am now, or hinder my development by providing me with incorrect reference positions? I'll never know, I guess, but I can't imagine having not read it.
Just do whatever you think is improving your game. It's all you can do, anyway.