Plug your gaming PC HDMI into the Game Capture, then from the Game Capture HDMI out to your monitor.
Plug the Game Capture USB into your second PC, open OBS, and add it as a source.
On your Gaming PC, install voice meeter. Set the default audio to Voice Meeter. In voice meeter, select A1 as your headphones, A2 as the Elgato HDMI audio.
Plug your interface into your streaming PC, go into the OBS audio settings, and select the mic as the interface.
:)