Right off the bat, this has much better performance on my laptop than Slack; Slack really spins the fans. Also, that extra layer of organization provided by the thread column was needed badly. I personally was hoping for tags and tag-groups in Slack, but this should also do nicely.
We have been using Slack as a UI for our backend services, for example, and it is a great way to present reports and alerts, and offer basic controls to the relevant person. For me, whether or not I actually adopt Twist will depend on how easily I can interact with it from my own software.
I would suggest making the integrations page easier to find - I had to troll through the Zendesk archive to find it, even though it is a core feature. Also, a link to the API docs on the help page would be nice. (Edit: Didn't realize until now that integrations are at the channel level, not the top level.)