If you are interested in the actual reason that line drawings are understandable to us, there's a readable scientific paper on it here, but suffice it to say it has nothing to do with a tiny rotoscope artists in our heads.
However there are many very useful insights in the Book of Lenses. One that I found particularly helpful when developing a game board was the idea of thinking of a game space as a series of zero dimensional cells. The below image is of two diagrams I created. The left shows my first attempt, and the zero dimensional diagram of it, and the right is the revision I made.
Particularly because I am working with an irregular grid, it was difficult to see how the spaces related to one another. Removing the extra dimensions made those relationships very clear and helped me to evaluate what I liked and didn't like about the design.
One very interesting concept Schell discusses is the possibility for this type of diagramming to work with imaginary spaces. For an example he shows a diagram of the game twenty questions. One space is the mind of the answerer, another the mind of the questioner. Another space, the conversation space, exists between the two. I think this is a very interesting way to think about game spaces, and I would like to explore it farther.