Just going to add a little missing info here. The vid shows you basically how to remove the handle. However, to get the lock off you need to undo the three torx bolts and move the actuator and door catch away from the back of the inside of the door. You will need to disconnect the harness too, which require a small flat head screwdriver to raise the red locking clip.
To remove the barrel you need to manipulate it from the outside while holding the actuator and raising it. It is now best that you have the new lock ready to fit, in arms reach. That way the rod stays in a good spot and doesn't come off at the bottom. the lock is removed from the outside of the door.
Getting the barrel back in takes patience to not damage the paint or the seal. Once it is back on you need to fit the long part of the door lever and the barrel at the same time, both need to be cocked upwards (the right side of the lock and the left side of the handle. This is because if you push the lock in first the lever won't hook into the mechanism. If you get the lever on first the lock jambs.
Once that is done you're right to fit the lock cover as described in the vid.