Obviously, you can use window / monitor capture and capture that. Likewise, you can add a browser source and crop it there.

However, is there a way to capture the video directly? Instead of getting the entire page, just get the video stream?

My guess is the cleanest and easiest way to do so is to run the desired twitch stream through VLC player (which is superior quality anyway) and then use window capture on the VLC player.

in theory adding https://player.twitch.tv/?channel=channelname would work as a browserSource with either &!mute (not muted) or &mute (force mute) at the end because twitch player is funny like that and loves to forget your volume options for popouts. The VLC method is prefered as you can choose a quality that runs stable and it needs to, because livestreamer is very bad about losing connection.