The Rift and Rift-S are 99.99% compatible. There is only really 1 difference that may affect game compatibility: the controller capacitive sensors. (There are differences like resolution, frame rate, haptic style, etc, but they won't stop games working). The Rift-S controllers are missing a little circular area next to the buttons. This is a capacitive sensor that can sense your thumb and change your thumb pose on the avatar model. Other than affecting how you give a thumbs up gesture, I don't know any game that uses it for something important.
Basically all games that work on a Rift will work on a Rift-S and vice versa. They may have a different experience (Rift-S is worse in dark games, Rift CV1 is worse at resolution, Rift-S is worse at haptics, Rift CV1 is better tracking, Rift-S is better at large tracking area) but they run the same games. They both use the same SDK and runtime software.