Thanks for the vid. That's rather strange. Instead of opening up Playground to test the device, could you try opening up the visualizer by right clicking on the Leap Motion Control Panel icon? Take a screenshot of the visualizer with your hand over the device.
Another thing you can try is reinstall the WinUSB drivers by running dpinst64 located in C:\Program Files (x86)\Leap Motion\Core Services\Drivers
Since it seems to be working on one machine and not the other, it definitely sounds like some sort of software issue. Reinstalling Windows may fix the issue for you but I'd like to avoid that if possible and use it as a last resort.