I understand the normal version of newcombs perfectly fine, I understand the normal version of counterfactual mugging (or at least the wiki version of it) perfectly fine, I get that the transparent boxes are mostly the same if you follow the logic , but in this case, the choice is presented AFTER you've picked boxes. "Here are two boxes. Would you like one or both. 'Both please.' Okay, also I'd like to inform you that if you pick both, you don't get the million. No backsies."
Saying that this is predicted in advance is weird, because there is no possibility of a meaningful loop: the moment of timeline separation is AFTER the choice has been made. The choice is set in stone. There is no possible change. You can pay, but it won't change a thing. Unless you were somehow determined to pay people in scenarios like this - which requires knowledge of scenarios like this.
In the original version, something happens, and then the losing you is contacted and asked whether you'd want to pay. And you'd be able to choose at that point, and even think about it. And then it turns out this was all a simulation and because you paid, the winning real you gets paid.
In this version, we could make it work by taking the result of the previous simulation (I flipped a coin you lost, pay me $100 or I won't pay $10000 if you had won), and then going through the prophet who either says you're fine if losing you paid, or that you're not fine if losing you didn't pay.
But what we cannot do is simulate this and loop it on itself. You are doomed in the future. You are always doomed in the future. There is no possibility of you being not doomed in the future. But, if you pay, then there is a possibility that you are not doomed in the future. That's a contradiction right there. If I accept that the statement about my unchanging future is false, then I'll pay because then I can go from 100% doomed to 50% doomed. If I accept that the statement about changing my future is false, then I won't pay, because you're a snake oil salesman, your cure will do me no good.
To fix this, the wording needs to be altered so that there is no contradiction and that there is a clear result of paying the money that will reduce the chance.
In short, I think this problem relies too much on UDT's ability to magically teleport between possible situations and failed to left a path for Time to take.
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Law might want to govern them, but the power of the state is limited. A court can't compel a computer that executes code to do anything.
Court can order computers dismantled. And I think there are methods for state to aquire property if it can be shown to be a "vechicle of crime". It is afterall the state that controls the monopoly on violence needed to enforce private property in the first place.