I think you still need Teensyduino. In the Teensy 3.X Project Template README.md, scroll down to the section "Where everything came from", everything listed (with the exception of 49-teensy.rules) comes from Teensyduino. I think you'll want to get the latest Teensyduino, install into the latest Arduino release that is supported by Teensyduino, and extract your files from there. This way you'll be in sync with the latest Teensyduino release. Or, you could wait until apmorton does this.
But since I've not done this myself, I look forward to hearing the details from Paul.
[UPDATE] I see that Teensyduino 1.32 was released on Dec 9th, 2016. The newest update in teensy-template that I can see was on Nov 14. This is why I suspect that teensy-template is not up-to-date with the latest Teensyduino, which is version 1.32.