I can name a few first-world democracies where multiple members of the same family have been elected heads of state.

Of course and a monarchist would expect such things to generally work out quite well on average. My point was that first president was royalty, his family had strong enough social capital to reach for power once more decades later which suggests strong background influence during the presidencies of Quett Masire and Festus Mogae. Note how the former of those was Vice-president under Seretse Khama and how Ian Khama served as Vice-president under the latter. If that family does not consider the country as something like a family business I don't know which one does.

Also that the De Beers company likely has quite a strong role in the governance of the country it doesn't need to share with many other corporate interests possibly approaching the United Fruit model, if this is so this is a very well run instance of that.

Moldbug's theory of government in action? He seems to think so.