If its anything like my corp, Twitch only gets a small discount, if any at all. It's expensive regardless. Network bandwidth alone is probably in the $20+ million a month range.
Well, that's sort of the problem here right; yes at AWS retail you are paying $20 million a month for traffic, but the cost to AWS isn't anywhere near that, in fact how AWS charges for traffic doesn't match to how it incurs costs at all. And in general having desirable services like Twitch and of course being ginormously huge means people want to peer with you and you have more leverage in those peerings, making them cheaper.