The main character goes from running to walking once the left analogue stick points directly upwards. Any slight movement to the right or left on my Xbox one controller makes him start running again. On my Xbox 360 controller the issue is even worse, with a larger degree for this strange 'running to walking' issue.
I'm honestly suprised more Xbox controller users who use PS Now have not commentated on this huge issue with one of the best PS3 games.
If you are surprised that a PS3 game does not work properly with an XBox controller that did not exist when the PS3 game was released, then you don't understand how PlayStation Now works. PlayStation Now never supported third-party (meaning non-DualShock 3 and DualShock 4) controllers. That means that a third-party controller might work with some PlayStation Now games, but if it does not work, then there is no reason for you to be surprised about it.