I assume you didn’t install fastboot yet neither on your Linux nor on your Windows machine, because it’s not clearly stated in the instructions. Correct?
On Linux Mint you should install android-tools-fastboot.
The command should be similar or same to
sudo apt-get install android-tools-fastboot
(I’m on Ubuntu, that’s why I’m not absolutely sure about the correct command)
After that you should connect your phone after booting it into fastboot (Power + Vol-) mode (USB debugging has to be activated).
If you already have installed fastboot please type the following to verify if your phone is correctly detected
sudo fastboot devices
Also, could you please state the complete error message you receive when the script on your Linux machine aborts?