Hmm it looks to me like just fancy on-chain caching. As far as I can tell, it doesn't solve the halting problem, because it requires someone to run the script with given inputs off-chain, and give the outputs.

So, by all appearances, it'll work for any script that *does* halt, but it'll probably get nonsensical for any non-halting script+inputs.

That's just from my cursory skim of the paper, so I'm open to correction if I'm missing anything here.