This project uses timer2 (presumably for PWM for IR output in xmitCodeElement), which is not available on the ATTiny85. This means that it will not run on Arduino-compatibles based on the attiny85.
One workaround could be to outsource the IR output to something like the IRRemote library, which does support ATTiny boards.
Specifically, I was trying to run this on this Adafruit Trinket.