To stream games to your PC, you need the tier of PlayStation Plus. Extra tier subscribers typically cannot access cloud streaming on PC — this is a Premium-only feature in most regions where the service is available.
If you're committed to the absolute best experience, consider picking up a used PlayStation 3 or PlayStation 4 console. God of War 3 (and the God of War 3 Remastered version) run natively on those systems with zero lag and perfect performance. But if buying a console isn't in the cards, the cloud streaming method will get you through the gates of Olympus. how to play god of war 3 on pc without emulator