I have the same model cameras that I purchased back in January, and I never found a 3rd party application that would work with them, or any way to access them except via Zmodo applications or hardware. As I understand it, these recent models use a proprietary streaming protocol.
Before I gave up and purchased a kit with a network video recorder (on sale for less than the NVR alone), I did confirm that manual recording from ZViewer worked, but I never checked into the motion recording, as I’ve found the motion detection of the cameras to be hit and miss. I checked my ZViewer software just now, and I noticed the same result as you found: “No storage medium”, and the box is greyed out (but checked). I suspect this setting may only apply to Zmodo cameras that have onboard storage (via a micro SD card).