I had a look at it. Honestly speaking, it does not really add anything new. Most of it is common sense, at least by the standards of this forum - most of the reasons for imbalances identified by the authors have been discussed for ages here.
(On a side note, I happen to own a book written by the main author Bruno Frey on the Economics of Art - so at least we can't blame him of being completely ignorant about the subject).
Their conclusion is "The empirical analysis, which shows that inclusion on the List is systematically correlated with economic and political factors unrelated to what "World Heritage" is claimed to be, suggests that extraneous factors play a significant role."
A few less thorough aspects I noticed (though I really just glanced quickly through it):
- when analysing the variable "years of high civilization" of countries and their correlation with number of cultural sites, the authors use a list by O'Brien which has the following 16 "high civilizations": Mesopotamian, Arabian, Phoenician, Persian, Egyptian, Ottoman, Jewish, Greek, Occident, Aegean, Roman, Byzantine, Indian, Chinese, Mongolian, and Japanese. You will notice a certain bias towards Mediterranean civilizations, the complete lack of any American civilizations, the lack of sub-Saharan African civilization - and even the lack of South East Asian civilizations (except if they are subsumed under "Indian" or "Chinese")
- a correlation is highlighted between Democracy and Number of sites on the list. This is attributed to the fact that elected politicians may have a desire to wow their voters by getting a WH accolade and thus get reelected (as you certainly noticed, this has been a major topic in many election campaigns in Europe recently...). It fails to acknowledge that some dictatorial states have actually even more reasons for wowing their masses with such accolades as substitute for granting them freedom, etc. China and Iran come to mind (the latter currently seeming on a World Heritage blitzkrieg, if we look at how fast the Iranian tentative list increased in the last years, and how many sites they managed to inscribe lately).