Meaning of P=NP? depends on space-time geometry ?
P=NP is a well-defined mathematical question which does not depend on space-time geometry. The question "which problems can be solved by computations that are tractable in this universe?" may depend on physics, and the answer does indeed appear to change in hyperbolic space or with quantum mechanics (e.g. quantum computing). However, this doesn't affect the P=NP question.

In fact, one of the first reactions of a theoretical computer scientist would have to your reference is: "What complexity class can be computed by a cellular automaton in hyperbolic space?" If you redefine complexity classes when you change to hyperbolic space, it becomes much harder to talk about this question.

And if you look later in the book, the author defines P$_h$ as problems solvable in polynomial time on a hyperbolic cellular automaton, and proves P$_h$=PSPACE (and NP$_h$=P$_h$=PSPACE), so even the author isn't really taking complexity classes to change in hyperbolic space.