Hey, I currently know of the following ways to get sound on your second pc:
1. Gaming PC-> Speaker output(green port) gets a Y-adapter cable to connect your speaker AND a 3.5mm Stereo cable that goes to the IN port of your live gamer hd.
Alternatively you can connect the second cable also to the blue port on your streaming PC instead of the Live Gamer. On your streaming PC you would then set your Line-In to listen to your Speakers, or select the Line-In as the Auxillary Sound device in OBS.
2. Gaming PC-> green port -> 3.5mm cable to IN port of live gamer HD and to the OUT port of live gamer you connect your speakers
3. Gaming PC-> sends Audio over HDMI -> HDMI connected to Live Gamer HD (you have to clone the Sound on your gaming pc to still hear it on your speakers)
4. a way I currently dont remember :) for example using Teamspeak/Hardware Audio Mixer/etc. etc.
Hope this helps you!