I downloaded Twine from the main site today.
I made sure System Preferences, Security & Privacy is set to install apps from anywhere.
I tried the instructions on this page, OSX Daily
I tried the instructions in this thread here at Twinery link, but Twine did not automatically open, and I still get the "Verifying "Twine"..." message when I click on Twine. I did it three times, restarted, same problem.
Update: Current workaround is to download an older version - 1.4.1 - from Toms Hardware: link