There's good reason to believe in a connection between airtime purchases and wealth. Mobile service providers throughout Africa allow their customers to transfer minutes between one another. In Côte d'Ivoire, such transfers are especially easy. The result is that airtime is used as currency in Côte d'Ivoire, Ghana, Egypt, and other countries. Airtime goes beyond being a proxy for wealth. In a sense, it is wealth.
There is a certain irony in studies such as this one. The main reason to do them is that, in countries like Côte d'Ivoire, government statistics can be spotty and unreliable. But the absence of solid statistics means the researchers have no real way of validating their results.
Still, as the map suggests, they're probably on the right track.