It seems to remember the last desktop mode (extension) even after you detach your primary monitor.
Could you please try the following workaround:
– attach your primary monitor
– connect the spacedesk viewer
– switch to projector mode / second screen only via display switch (Windows logo key + P)
– detach your primary monitor
Try to restart your primary machine this time without your primary monitor attached and just try to connect your spacedesk viewer.