I’ve also tried running the installer on a headless Linux VM but it complained that there was an X_11 variable not set so I’m assuming the linux version cannot run without a GUI.
If you are comfortable with this setup, you can install avrdude (for example: apt-get install avrdude) and update the firmware from the command line without a GUI.
For hardware version 2.1:
Remember you still need to enter bootloading mode, instructions here:
To enter bootloading mode: turn off the controller; press and hold pushbutton B2 while plugging in a USB cable; then release B2 within 2 seconds after inserting the USB cable. The screen should remain off.
The following command would work (assuming the file, firmware2.0.9.hex, is in the current working directory):
avrdude -c usbasp -p m644 -F -U flash:w:firmware2.0.9.hex