Although you CAN use a PS4 controller with the game, it is currently optimised for Xbox controllers - you might find a few inconsistencies. The most notable of these is that certain buttons might not match up - The A button is Square, for example.
In order to use a PS4 controller with the game, you'll need to connect the controller with the USB cable that came with your PS4 system. Then give your system time to find and install the necessary drivers - PS4 controllers should do this "out of the box" so to speak, but this might depend on your OS.
IMPORTANT: at this stage you should make sure the power on your PS4 system is completely unplugged - there are stories of systems still receiving input and buying hundreds of games by accident.
Once drivers are installed correctly, make sure the controller is on and boot up the game - you should find yourself able to play, although as mentioned before the controller will likely have some mapping issues.
Hope this helps, and I hope you enjoy the demo! Take some screenshots :D
- Niall, Torque Studios