I would describe it at showing how poor/unproductive the rest of Botswana's economy is.

Or is the theory here that De Beers somehow keeps the part of the Botswanian economy they don't participate in poor/unproductive?

De Beers was founded by the guy whose colonial governance helped make the region as economically depressed as it was. When Debswana was founded, De Beers was taking something like 85% of the profits from Botswana's natural resources. That's like if I burned your house and farm down, then a few later I discovered oil on your land and offered to help you drill for it in exchange for a little over an eighth of the profit. What choice do you have?