The key will lie in identifying the twitch traffic, or the game traffic, and policy routing it separately. How you do that is up to the services in question.
If all the twitch traffic goes to a specific IP, or if the game traffic goes to a specific IP, then you could match that, or match by port numbers perhaps.
As long as you can match the traffic with a firewall rule, you can make that happen, but the specifics of that depend entirely on how the services operate.