I'm not a lawyer, but my understanding of GPL is that the requirements are only triggered if you distribute your software
Twitch's back-end code (server code) is never distributed to customers/users, so it ought to be completely fine to use GPL code in any way they want
Twitch's front-end code (desktop apps, web apps, mobile apps, etc) would count as distribution, so any use of GPL code here would have to comply with the license
If an open-source developer wants to protect their code from the back-end code loophole (increasingly important as software-as-a-service becomes the dominant software use case) then the Aferro GPL (a.k.a AGPL) is probably what you're after, as those requirements count network connectivity as distribution