It appears that Sony is now giving gamers a chance to rent games from the PlayStation Store now.
The PSN received an update earlier this week and it looks like game rentals came with it. MP1ST saw a game rental option when they were browsing for Catherine on the PSN. There are options to rent for one day, seven days or even 30 days.
It seems as if the rental option is a part of the PlayStation Now service.
This option has been found for the North American PSN only at the moment. Hopefully it will roll out for other countries soon as well.