It might not be clear from the last chapter, but the book doesn't claim that time doesn't exist.
To paraphrase (but use the same example because it is funny): time doesn't appear at the fundamental concepts in physics. Cats also don't appear at the fundamental level of physics. But cats exist. Time (and our perception of it) must appear somewhere as a emergent feature.
To paraphrase (but use the same example because it is funny): time doesn't appear at the fundamental concepts in physics. Cats also don't appear at the fundamental level of physics. But cats exist. Time (and our perception of it) must appear somewhere as a emergent feature.