Game Developers do it in a few ways.
- in game via the oAuth flow (usually implicit)
- or the game links to your backend and the streamers can link their account via your website, and the game just loads up that association. (borderlands does this, you login to shift in game, and on the shift website outside of the game you link shift to twitch for example)
- Or they might just need the broadcasters channel name, so you could just use a blank text field and ask the streamer for their name, then you don’t need oAuth at all.