The argument is that simple numbers like 3^^^3 should be considered much more likely than random numbers with a similar size, since they have short descriptions and so the mechanisms by which that many people (or whatever) hang in the balance are less complex.

Consider the options A = "a proposed action affects 3^^^3 people" and B = "the number 3^^^3 was made up to make a point". Given my knowledge about the mechanisms that affect people in the real world and about the mechanisms people use to make points in arguments, I would say that the likelihood of A versus B is hugely in favor of B. This is because the relevant probabilities for calculating the likelihood scale (for large values and up to a first order approximation) with the size of the number in question for option A and the complexity of the number for option B. I didn't read de Blanc's paper further than the abstract, but from that and your description of the paper it seems that its setting is far more abstract and uninformative than the setting of Pascal's mugging, in which we also have the background knowledge of our usual life experience.