How about export these registry locations from OS where Webcam is working, and import them to the problematic server? If this will not help, I can recommend delete these values at all, reinstall the program and add them again.
Can you test your server and camera with USB for Remote Desktop? Install it the same way as Webcam for Remote Desktop on local and remote computers and check if the camera can be redirected.
Understood. I think you should uninstall USB for Remote Desktop and seek for possible differences in configurations between your two servers. Maybe it's RDP preferences or user account policies.