as far as I can you need to manually edit /DietPi/config.txt and add
dtoverlay=hifiberry-dac
... and probably comment out:
dtparam=audio=on
basically, you need to follow the manual install steps described at:
http://learn.pimoroni.com/tutorial/phat/raspberry-pi-phat-dac-install
and verify that all the changes you make have not been wiped at the next reboot, due to the RAMdisk based system.