No, the death of the universe he referred to was not inferred from the behavior of time within the space-time manifold (block) itself but rather the laws governing the finitude of thermodynamic energy across the universe and the extrapolation of that reality across increasing time.
In order to reference the death of the universe, he is presuming the shape of the universe to be flat or hyperbolic. In his model, the cube would represent the flow of time and worldlines of all objects moving from second to second (like watching a video).
He did not need to reference the death of the universe. Many can believe in an closed (spherical) universe and still hold to the block universe theory. I think he referenced it to drive home the "watching this video" analogy which would include a definite end. But he probably believes it as do all who interpret the acceleration of the expanding universe to mean it is basically geometrically flat.
But the shape of the universe is not a necessary condition for this model and the heat death of the universe is not a necessary consequent either.
One could hold the shape of the universe to be "spherical" and without "end" (not infinite but closed) in shape while holding to the block universe theory of time.
In that model, the universe would not "die" but start to contract. Those who hold to block universe would say that the present for different observers is a time-slice of the 4D universe and when it starts to contract, the present moves forward as always.
The citation that some A-theorists hate (because they prefer QM to allow effects to precede causes especially within "big bang" singularities):
- Events in our world are causally related.
- The causal relation is inherently asymmetrical. Effects depend on their causes in a way that causes do not depend on their effects.
- This asymmetry is only possible if a cause's effects are not real as of the time of their cause.
- Causes occur before their effects. "X is earlier than Y" means roughly that some event simultaneous with X causes some event simultaneous with Y.
- Our universe must therefore be a growing block.
Dainton, Barry (2010).
Time and Space (Second ed.). Durham: Acumen Publishing Limited. p. 77.
NOTE: I am merely reporting positions as to time as it relates to us (creatures). This is not an endorsement of the current thinking in block universe theory - although I do object to a lot of A-theory for the anti-rational implications that are sometimes subtle, other times bolder.
Nothing here undoes the doctrines of God, His attributes or the stark Creator-creature distinction. If anything, the deeper one looks, the more and more one must marvel at the gulf of knowledge between God and us.