I had two Word 2016 problems after updating from the beta: couldn't open files directly from Finder, and documents kept locking because the activation kept, well, deactivating. Curiously these occurred in Word, but not Excel.
This solution posted in the Office 365 forum here worked for me.
https://community.office365.com/en-us/f/153/t/358789
1. Launch Word
2. In the Menu bar, Click Word then Preferences
3. In the General tab, make sure "Show Word Document Gallery when opening Word" is checked
4. Close the Preferences window
5. Exit Word
6. Launch Word
7. If you have a license, you should be greeted with a Get Started window
8. Click Get Started and follow the wizard.