You should still be able to stream Conan Outcasts as long as you have made sure Drops are enabled on your Twitch account. They should be enabled by default. On Twitch, I think the only category is Conan Exiles; there is not a separate category for Outcasts.
If you watch other Conan Exiles streams on Twitch, you should still be able to get drops, and then once the link is added to the game, you can link your account and get the rewards.