The paper takes a purely empirical approach (simulate an organization with given performance characteristics and promotion rules, and see how well it does according to an ad hod measure), and it doesn't even seem that its authors have understood why it's obvious that under what they call the "Peter hypothesis" -- which is not in fact quite the hypothesis Laurence Peter made, and neither is their version of the Peter principle correct -- promoting the worst performers is best.
The paper also considers a "Common Sense Hypothesis", namely that competence at different levels is strongly correlated. Unsurprisingly, the authors find that promoting the best performers works then.
Of course, reality probably doesn't quite match either the overoptimistic "common sense hypothesis" or the overpessimistic "Peter hypothesis". The authors apparently think that a good way to deal with this is to ask what minimizes your worst-case losses if you know that one of those hypotheses holds but don't know which. So they recommend either promoting at random, or alternating between promoting the best performer and promoting the worst performer.
It might be interesting to do a study like theirs using more realistic models of employee performance at different levels of the hierarchy, but I don't see much value in what they've done.
(Let me speculate mischievously that the authors are probably quite good at what they mostly do for a living; perhaps the apparent lack of correlation between that and their success in investigating the Peter principle is itself evidence for their version of the "Peter hypothesis"...)