I don't know how common the "tire guard" featured in the video is, but it seems like a damned good idea. It would solve the problem of split pieces flying off with explosive force. I'd probably pursue that idea posthaste.
My son joked that I could probably reproduce something we once saw in a cartoon, where the chopped pieces assembled themselves into a log cabin.
It seems this leveraged action (which is absolutely awesome, by the by) would necessitate the use of a tire even more. Beware of windows, cars, etc. without one.