This works but could do with an update to make it easier to use/ set-up.
When you first install and then browse to Appearance -> Widgets and drop the new Genesis Latest Tweets widget into e.g. a sidebar, a link is shown to go to the settings. Clicking on this link doesn't work and you get a 'You do not have the permissions to access this page' error.
However, going to Genesis -> Latest Tweets works fine. :)
Once there, it isn't entirely clear what to do because the labels shown are no longer up to date and there is now another 'Create access token' step to complete first on https://apps.twitter.com before you have all the info you need.
Once you've clicked that button and created an access token, it isn't too hard to guess what to copy and paste:
OAuth Consumer Key = API key
OAuth Consumer Secret = API secret
OAuth Access Token = Access token
OAuth Access Secret = Access token secret
After copy pasting those and hitting save, go back to Appearance -> Widgets -> Genesis Latest Tweets and you'll see there are now widget options to choose/ complete :)