IANAL but it would go something like this: Twitch has IP addresses of the trolls, but no way to tell their real identity. So they file the lawsuit and then use it to subpoena the ISPs assigned those IP addresses to get their client information.
It's not enough to be used as evidence in court.
Most likely did the majority of the bots use proxies and VPNs, which may or may not provide additional information about their customers, but even then it has to be proven that is was the same user that did the acts which is very difficult.