>Do you need to download peertube to watch streams over it?
Nah, PeerTube is just the server software, just like this imageboard uses LynxChan. You just bring your web browser (or other client, like youtube-dl or a mobile app). It's kind of like a self-hosted YouTube, for a shallow analogy.
by default it uses peer-to-peer streaming to take the load off of small servers if something gets wildly popular, so if you aren't using a VPN and are worried about the zero
other people watching being able to see your IP address (strange combo but whatever), click 'My Settings' and turn 'Help share videos being played' off (you don't need to be logged in).
Here's one of the many instances (this is the official demonstration one, closed off to new user registration): https://peertube.cpy.re/w/mRN2Js6YT3igjiB4f674Ds
And an example of one with user registration: https://peertube.linuxrocks.online/videos/overview
>Musical DMCA aside, what's the issue with streaming on twitch exactly?
I won't get too autistic if we need to use it, but basically supporting a closed-source, corporate, user-abusive service isn't something I enjoy doing. Imageboard users have an increased tenancy to reject mainstream social media and things like Discord; in fact privacy concerns are a reason why many people move to anonymous imageboards in the first place.