Most game replay systems work this way - they store the chain of user inputs, and then just resimulate it in order, with the same random seed. Thats the main reason they don't give you the option to rewind the replays and you have to start over.
This game just has multiple simulators running through the chain of commands at the same time, a "movable" simulator (the player's view) and the ability to modify the chain of commands. Once you can distill the idea of "moving backwards through time" into a command, it can be added to the chain of commands and be deterministically simulated like everything else.
For the game replay system you describe, the only requirement is total determinism. That's not the same as what is being shown here, where the "separate simulators" are actually not independent.
Both you and stcredzero are significantly underestimating the complexity introduced by the chronoporters. Without those, you'd be right, but those introduce additional complexity that I would despair of getting right with imperative programming.
It always looks simple when you just look at a demo. It's much harder when you go to actually do it.
This game just has multiple simulators running through the chain of commands at the same time, a "movable" simulator (the player's view) and the ability to modify the chain of commands. Once you can distill the idea of "moving backwards through time" into a command, it can be added to the chain of commands and be deterministically simulated like everything else.