I can't see the video, YouTube decided to die, but from your description, the addon you seek is "JIM's Cooldown Pulse" or something like that. Whenever an ability's cooldown is complete the ability's icon "pulses" into view on the center of the screen.
At first it is a little annoying, but after a while you get used to not having to let your eyes away from the battle. Combine with a good HUD addon (such as MetaHUD) and you can concentrate on the battle completely without moving your eyes.
But, as with everything else, what is good for me might not be good for you, such is life.
EDIT: I've seen the video now and yes, that is
JIM's Cooldown Pulse.