Yes he does. He is moving then issuing an attack move command on the same spot. This is called Kiting your opponent. It's effective because you use the cooldown between attacks to move, effectively shooting at the same rate (if done perfectly) while still being able to move.
You can see it yourself in that video that he links. You just need to know that when there's that green arrow indicator that it means a move command (ie right click) was issued. Whereas if the indicator is red it means an attack move command was issued (ie 'T' left click on ground).
Ideally you want to attack move back towards the direction that the enemy is so that those units out of range will go back to attack as well.