Trinket not listed in Boards menu

Any idea why the Trinket isn't listed in my boards menu?

You probably didn't install the Adafruit board support package, as described here: Arduino 1.6.x IDE | Adafruit Arduino IDE Setup | Adafruit Learning System
(The fact that you need to install something other than just the normal Arduino install IS buried surprisingly deep in the Trinket tutorials. Sigh.)