Roman empire vs Rome city
I think in the following sentence the first "Rome" can mean "Roman Empire" but the second "Rome" means "Rome city". Am I right?
Sentence:
Presentations of military success in Rome also derive from Greek and Hellenistic models. The ten-metre-wide marble Ara Pacis Augustae (13–9 bc) in Rome commemorates the pacification of Spain and Gaul (France).