Well, the only thing I could think of is debugging why it isn't working. See if there are any logs in the game folder. Start the game executable via console and see what the output says. This way I have discovered some missing dependencies for some game on Linux. When the game crashed it left a good error message in the console.
I did research on that message and figured out the missing packages. Installed them and the game worked. Sometimes it also a matter of permissions.
However given that Linux on PS4 is not entirely working like on a real PC the games might simply not work.