The reason is that a "single lens reflex" camera, by definition, uses a mirror to reflect light that's passed through the single lens into the viewfinder.
The Domirex uses a number of small mirrors to redirect the image to the viewfinder, rather than a single large mirror along with the bulging pentaprism typical of 35mm SLR cameras.
[2] The iris diaphragm and the leaf shutter are mounted behind the rear lens element.
[3] The system has the disadvantage that focusing must be performed using only a small fraction of the available light.
[4] The Domirex was never put into full production, and apparently only had a fixed, 57mm lens.