That sounds right - the airport code is CPO which should mean Copiapo
As for who would be using the airport - well tourists do visit the Atacama a lot, but tend to gather around San Pedro de Atacama, up near Calama (check this map to get an idea where that is!)
Much more likely this airport will be to serve the city of Copiapo - with the distances involved travelling in Chile, the plane is often going to be preferable to a long (10 hours from Santiago?!) bus journey. And it look like its in the middle of nowhere because, um, there's plenty of space in the desert and no need to build the airport right on top of town!
Bear in mind that because of the shape of the country, LAN actually operate a lot of their flights as multi-stop flights, thus overcoming problems associated with low demand in individual cities.