Alright, so... a couple of things.
1. I don't know the actual name for this trick. I saw it on Guy Wright's video "Punch Line," so I figured it would probably do Guy and the trick enough justice to simply call the trick "Punchliner."
2. Technically, I'm not doing the trick exactly like it's done in Guy's video. At the point of the trick where you swing over your thumb, Guy actually swings the yoyo over his thumb and lets it bounces off of the double strings, instead of just sort of letting the yoyo hang and then swinging it the other way. Not only that, but as he swings the yoyo around, he kind of pinches his thumb and middle finger together and then separates them right as he swings around his thumb either direction. You can watch his video >here< to see what I mean (the trick is at 0:52 in the video, but watch the whole video, it's great).
The way the trick is taught in the video still, in my opinion, holds true to the effect Guy Wright was going for with the trick. The differences are only minor details.