Can I play purchased PSN games without a PSN subscription?
As of now you cannot play GTA 4 on PS4. It was originally released on Xbox 360, PS3 and Windows PC. While current generation Xbox is backward compatible (so you can play Xbox 360 games on Xbox One), it's not the case for PS.
Some PS3 games are available via PS Now subscription service, but I don't see GTA 4 in that list.
And in general, if you buy any other PS4 game from PSN store you don't need any additional subscriptions - it yours, play whenever.