Everyone is confusing strafe jumping, circle jumping, and circle-strafe jumping.
Strafe jumping is something you can do without touching your mouse. It's jumping while running forward and holding the strafe key down a split second before you jump. For ranger, this takes his speed up to about 380 from the normal 310. It's not great, but it's faster than running or jumping with the strafe key. Simple strafe jumping.
Circle jumping is something you can do from stationary. From standing still, if you add a split-second of circular running before a strafe jump, you can get ranger up to about 450 on the first jump.
If you do something similar to the "flick" from this video while repeatedly strafe jumping, you are simply combining strafe jumping and circle jumping on every jump. This gets you up above 600 if you do it right. The flick is just a clever way to add the split-second of circular running inbetween every single jump. The physics engine is simulating centrifugal force from the circular run, and holding the strafe key adds a bit of extra to it. This is where the "fishing" analogy used in this video comes from....because casting a fishing rod uses centrifugal force.