I am pretty sure that for the stream to pick up party chat you need to have the chat audio coming out of the TV. The only way to do this is to have a mic(Blue Snowball) plug it in to the PS. Then you need another mic/headset to plug into your computer. This should give you both your audio and your party chat audio. I personally dont even bother with it because it is too much of a struggle, because it is hard to hear my teammates coming through my TV when I also need the game audio to play.