Sure but Twitch is here suing people in a real court. It's not about whether Twitch is forced to host your speech or whatever. Here the government is getting involved.
To get people off their platform they have to serve a restraining order. If someone is hiding their identity the only way to get it is through the courts. For obvious reasons ISPs don’t give that info out to anyone who asks.
Doing that costs them a lot of money, so why shouldn’t they also seek to recover those costs?
That's exactly what it's about.
>Here the government is getting involved.
Which is not the same thing as the government abrogating anyone's freedom of speech, fairly obviously.