I think that reading a book without a board is a skill that you can develop as you practice it.
It certainly helps to have actually attempted to keep game scores yourself and then go over them afterwards and try to figure out what really happened in your games.
It really depends on the book. If there are many diagrams and a lot of text, I read them while being in the train or so. With others I need to use a board.
The pleasure of moving physical pieces on a physical chessboard is irreplaceable.
When I read a book, I always have the chessboard and the pieces next to me. Even reproducing the various positions that are created move after move is very pleasant ( and more useful, I think). After trying to calculate by myself, I always reproduce the moves on the board.
I tend to do it so that I think of different moves I could play and then pick one and only then continue with the book and see what the explanation is for the move provided in the book. I find this approach works very well.
I haven't read a single chess book in my life. Books just never worked for me. I'm a visual learner
I haven't read a single chess book in my life. Books just never worked for me. I'm a visual learner
Having a physical board along with the book makes it very visual I think 
The key is to find a method that works best for you and aligns with your goals.
I'd say chess books may be a waste till around my level, though I'm not too qualified as a rapid 2000. There is so much free material online on youtube and chesscom
So for a long time I have stayed away from chess books because reading the annotation seemed hard to me. Lately, however, I have been reading this one book and got into it. It seems to be fun to take my physical board and play the moves discussed in the book.
How do you read chess books? Do you play along on your physical board or can you picture it all in your head?