The animation splits each guy in half, but takes a small slice of each one to assemble a 13th guy. It's difficult to see because their relative vertical positions in the drawing makes it nearly impossible to see which portion each guy loses/contributes. Also, the nature of the drawing gives fewer visual cues: it's cartoonish, all of their hands are behind their backs, etc.
The following images are by Matthew Baldwin at Defective Yeti.
Here are the guys, identified by color and numbered in terms of the order they appear from left to right in the initial configuration, but rearranged in terms of vertical position:
Pretty basic: each guy is sliced in two and the upper part is moved to the right. To make the puzzle, the creator mixed up the order of the guys.
Still not making sense? This image shows each individual dude and how large of a "slice" he contributes:
Voila: 12 guys that are 11/12 complete, and a 13th guy that is 12/12 complete.
There's an awesome graphical algebraic representation of what happens, about 6/12 of the way down this page, by Jon Parish.
Props to glowing_fish, sanguinity, and bernmarx, all of whom are smarter than me, and figured it out without help.
OK, back to work.