For what it's worth, I installed DietPi to check it out for myself and the problem is that /boot/config.txt is not a resource you can edit directly.
Instead, you need to edit /DietPi/config.txt and add the device tree overlay there.
Incidentally, I find it obnoxious that a distro can build so heavily on Raspbian to the point of masquerading as the parent distro. If it did not you would have saved yourself a bit of time when our installer had refused to do its job since your environment was not supported.
... either way, it's definitely possible to get the pHAT DAC working on DietPi, but you shouldn't expect the phatdac installer to set you up, it was not designed for this I'm afraid.