From watching the video and reading one of the papers, I get the sense that the theory being described doesn't work in the usual way. For example, reading the paper it talks about "future inputs" determining what happens, which seems impossible if you need to have the entire state specified for each time slice without need to reference other time slices. Instead of having a specific state for time t, and being able to evolve it forward/backward to other times, it is instead applying constraints across spacetime?

In principle, allowing yourself that kind of flexibility could be enough to model quantum mechanics. But I'm not sure why I'd want to do it that way instead of the existing ways. It's not particularly philosophically appealing to me, and objectively speaking it looks like they don't yet have a concrete mathematical model that actually reproduces quantum mechanics. But maybe I'm just ignorant of the latter part's existence.