If it is a rubber mat (shelf-liner, maybe), I use something very similar when I play my lute, lying the mat across both legs, because the round back of the lute won't stay put (I hold it like a classical guitar), and the rubber mat holds it quite firmly in place as it basically sticks to my legs! I have met a few other lutenists who use something similar to hold their lutes steady. In fact, now that I mention it, I've also seen a few guitarists who use a rubber mat across their whole lap like in that video. It is not a "support" so much as an anti-slip device to be used in conjunction with a support (or footstool). The danger (well, maybe that word overstates it) is that a rubber mat may leave marks on the finish of the instrument where it makes contact, but of course, having it not slip around while one is playing may be worth it.
And, yes, quite a nice presentation for the sale of that guitar!