They know their hardware. It's entirely possible that the 'capture device' only records internally, and will not provide a live feed over USB to a host computer. You may need to buy a different capture device that can do that. Something like an Elgato HD60S or S+ (not the non-S! you need a USB 3.0 capture device; 2.0 usually have around 2 seconds or more of capture delay, which makes working with them a PITA) would work, or you could go the NDI route.
For a capture device, you'd plug an HDMI cable into the Mac's HDMI out port, replicate your desktop to it. The HDMI cable goes into your capture device, then the USB from the cap device goes into the Windows machine. In OBS on the Windows machine, you add a Video Capture Device source, pointing at the capture device. That's it for video. Audio is MUCH more complicated, and a true pain in the butt, especially with a DAW in the mix.