How does this guy's example differ what what I am doing?
He is using lower voltages, but he still needs a common ground to work correctly. Basically what he is doing is rubbish as well. He doesn’t understand much.
Would that not create a ground loop?
I am not sure what you understand by a ground loop and why it should be bad but no.
how can I give it a common ground?
Connect the Negitave of the 20V charger to the ground of the Arduino.