Note that the Pocket Chain Saw company (Supreme Products) makes two versions:

http://www.unbelievablesaw.com/

http://www.pocketchainsaw.com/

Each has its own advantages/disadvantages.

BTW, note that the branch in the video has only 6 inches or so of wood above it. Try that with a standing (dead) tree, and you'll experience severe pinching (that would happen with most all saws).