I could not find anything showing that this particular video is a fake so I took my research in a different angle and looked up how quickly a chameleon can change National Geographic says it can occur in 20 seconds*. So the critter in the video has very impressive ability or the video may be slightly sped up. As far as having multiple colors at the same time. I've seen it done in person at a pet store!

I will let a direct quote handle how it works.

"Chameleons are born with special cells that have a color, or pigment, in them. These cells lie in layers under the chameleon's outer skin. They are called chromatophores (kro MAT uh fors). The top layers of chromatophores have red or yellow pigment. The lower layers have blue or white pigment. When these pigment cells change, the chameleon's skin color changes."

Chromatophores change because they get a message from the brain. The message tells the cells to enlarge or to shrink. These actions cause cell pigments to mix—just like paint."

http://magma.nationalgeographic.com/ngexplorer/0210/articles/mainarticle.html

I have also included another fun and interesting video for your pleasure.

Oh an Chameleons actually take a back seat to the Octopus

It is actually not true that chameleons change colour to blend in with its surroundings.
Reasons for chameleons change colour is as a signal, a visual signal of mood and aggression, territory and mating behaviour by molecule – they're molecular masterminds.
If you look at the skin of a chameleon, you find that they have several layers of specialised cells called chromatophores and these are cells that can change colour.

http://www.thenakedscientists.com/HTML/content/latest-questions/question/2634/