There is no deeper meaning behind Link not existing when the game is turned off. You are reading too much into it.

I am not sure what exactly I expected, but, for the most part, I didn't get it. Most of the philosophical discussions in this book are linked to the Legend of Zelda by the most tenuous of threads, relate the content of the game to philosophy in a way that is so meta that all meaning is lost, or are simply uninteresting.

In this book, Zelda is either being shoehorned into the philosophy or the philosophy is being shoehorned into Zelda. Many of the examinations also ignore or are ignorant of game design considerations in favor of philosophical considerations. This basically invalidates their work, as the design of the Legend of Zelda is an intrinsic part of its existence.

There was a single exception. The Triforce and the Doctrine of the Mean, written by Patrick Dugan is a fantastic example of what a volume like this should contain. He examines the purpose and usage of each part of the Triforce within the world created by the Zelda games and judges them using Aristotle's Doctrine of the Mean. This is interesting because it is confined to the game world, (it does not try to relate the Triforce to something outside of Hyrule) and it contains interesting observations about the way the characters in the Legend of Zelda are depicted based on how they use their piece of the Triforce. I would give this chapter by itself 3-4 stars and I would recommend you read only this chapter in a bookstore, rather than buying this book.