Exactly how are you defining a DAC? From your description, the amp IS A DAC.
Simply put, a DAC stands for digital to analog converter. You don’t listen to PWM. You listen to, must listen to, music as an analog event.
So that PWM signal must go somewhere, and the moment it becomes an analog signal you have a DAC.
I should also point out that Class D is an analog, but switched system. A purely PWM driven amplifier has complications of it’s own, especially how the lack of feedback is a challenge.
To borrow a term from marketters, this is a powerDAC.