Hmm I have no idea how the back end works sorry, but it is probably something to do with the twitch API. I don't think you have to look at the green screen background, just find a way a streamer can connect their account for you to read their chat. OR an easier option would be to make a web-app/twitch add-ons where the chatters can vote there.
I would also add 2 more options to the game, I think 3 options is too little. And a last thing you really need is live feedback. It would be way more exciting if you are a chatter and you're waiting to vote till the end, because you want to pick strategically, the biggest pile will not always be the best pile. But eventually everyone will wait till the end so it turns into pure chaos anyway :)