My goal is for my friend to be able to turn on his headphones and connect much like the 8bitdo is allowing me to with the controller.
Then you need to pair & trust the headphones BT first (via bluetoothctl), just like the gamepad was paired with the RetroPie Bluetooth script.
'm confused if the above lines are related to the adapter, why would it be referred to as retropie?
It's the 'local' BT adapter and the name is taken from the hostname of the system, that's why it shows as 'retropie'. Controller is also a mis-nomer, it refers to the BT local device, not the gamepad you have connected.