That is a definite fake, the Youtube videos don't work like that. they require prestige one prestige at a time (I know someone who did it, who I removed from my clan).

The reason I know this is a fake is because I just prestiged to prestige 20, and "Prestige Mode" shouldn't be greyed out when you click it to prestige. That image has been photoshop, probably. its not really that hard to do; quite simple.

Look at the pixels in the background and foreground, they are obviously from different images. the background is a low quality image while the forground one is high quality. Also the background image with the stats is faded, Showing it was edited before the foreground picture was laid on top.