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.
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?