The Rig Cam is a webcam pointed at the commissioner's monitor to allow managers and colour commentators to see the match as it happens without delay.
Due to Twitch's ~30 second delay, colour commentators would have a hard time to make relevant statements about what's happening if they were watching the same stream as everyone else.
While being somewhat of a ghetto set-up, it's less of a burden on the streamer's computer, as there is still just one application grabbing frames from PES, instead of two at the same time.
Skype is very well geared towards low-latency video streaming, as video chat requires low latencies to feel natural.
If you are invited to the 4CC Skype call before your team's game, it's most likely for the Rig Cam. The commissioner will expect you to mute your microphone during the call.
A capture card could replace the rig cam and be less ghetto, however, this requires additional hardware. Once a capture card is connected and set up correctly, it would most likely show up as a DirectShow device like a normal webcam, which means Skype could stream it.
Another possible improvement would be a re-streaming set-up. In this scenario, the streamer would stream to a re-broadcasting server instead of twitch. Said server would broadcast to twitch and also allow colour commentators and managers to see the game without Twitch's latency. However, the latency would still be one of several seconds, making this set-up less appealing than Skype video.