Yes! Xbox360 is default, so you have to configure your PS4 the controller (hit BACKSPACE at the start of the game). 

The game should work but with any other controller with enough button to complete the configuration.

If you have problems, you can try the xbox360 emulator like this one:

https://github.com/x360ce/x360ce#readme

Unfortunately this game does not support DS4.  

My DS4 works with every other game except for this one. This game does not respond to any DS4 buttons.