Having come from a background where I have played chess and poker to a fair level then I think that I have a pretty good idea on what makes a great backgammon player. There is a common evolutionary process that is taken to get to be a top player and I know full well what those evolutionary processes are. You obviously need to learn the theory and it is difficult to learn this in a sort of ad hoc way.
However just like in poker, there are very powerful gambling elements to backgammon and is why poker and chess players have become excellent backgammon players and vice versa. There are many factors behind why a top player becomes a top player that are very difficult to teach. Knowing theory and an intense knowledge of cube decisions are such factors and this is where computers really excel over human players because they can calculate cube decisions accurately just like chess computers can compute combinations far better than any human.
There are things that happen in a game that a computer program may find very difficult to pick up. Like your opponents attitude to risk for example and how that can change over time. One could also look at what you can “feel” your opponent is doing. Once certain players get in front then they can tighten up and their game play on the board reflects this. Or for example certain players who get the lead can take even more risks simply because they have a lead to play with. So psychology is a huge part of backgammon just like it is poker and this is what computers fail to come to terms with.
