I would say Sao Paulo is a conecting point but since they are outside the airport i say there is a Sao Paulo leg.
So the race could go like this
1- (Argentina) NEL (El Calafate?, Bariloche?, Ushuaia?)
2- (Argentina) elimination (Rosario?, Mar del Plata?, somewhere near Buenos Aires?)
3- (Argentina -> Uruguay) elimination (Colonia del Sacramento)
4- (Uruguay) elimination (Montevideo?, Punta del Este?)
5- (Uruguay -> Chile) elimination (Santiago)
6- (Chile) elimination (San Pedro de Atacama)
7- (Chile) elimination (Antofagasta)
8- (Chile -> Ecuador) NEL? (Quito?)
9- (Ecuador) elimination? (somewhere near Quito?, Cuenca?)
10- (Ecuador -> Brazil) NEL? (Salvador)
11- (Brazil) final elimination? (¿?)
12- (Brazil) Finale (Sao Paulo)
Seeing the route at this point it looks like a circle to me. So the next country could be ANYWHERE.