I have tried logging into twitch account and I have done 2FA, but the game geniue authentication didn't pop up. Instead, it just showed a home screen of twitch.tv.
To further this, while I have a ZenFone 6 and not a ROG 2, I encountered this problem as well when I tried to connect to twitch. I had hoped that the latest OTA (which I just installed) would have fixed it but instead it appeared to have removed twitch as an option entirely which was a rather disappointing 'fix'. I'm not sure if the versions are the same between our phones but perhaps something for ROG2 users to look forward to if we do.
Due to user-experience issues related to Twitch - we decided to remove Twitch-integration in Game Genie. If you need to use Twitch Live streaming feature; please use any of the 3rd party alternatives available to you via the Google Play Store. We are sorry for any inconvenience this might cause you.