First, do not believe what you read(see) on the internet. What you saw is a KD taking a rag and trying to eat it. I had that happen with croc monitors. Its not playing. It would be playing if the KD threw the rag back and took it again, over and over.
You see, you really need some evidence that the monitor is simply not taking the hankie. Monitors do take stuff.
Do they Play? that is a very hard question to answer. I keep lots of monitors and for a very long time(probably more and longer then anyone in the world) I keep them in groups and I see things that could be considered playing. Like large males, messing with my head. Doing these fake dives at my feet. They then back up and appear to laugh. Ok, they don't laugh, they just look at me as I dance around.(anyone watching this would laugh)
What I do not see is neonates playing(the ones that should play) They do practice behaviors, but do not do anything that could be consistantly called playing. Now consider, I have raised thousands, and of many species.
I also live in the desert and have lots of wild lizards around. I never see them play, everything they do is of direct meaning to their lifes.
I would love to think our monitors are somehow having fun or experiencing some joy. And I believe they do. But not from playing. They appear to take satisfaction, from accomplishing their day to day tasks. Yes, they exhibit a look of satisfaction, from a job well done.
Ok, I take that back, I have seen wild monitors(of many species) play with me. They are so good at escaping, they will actually taunt you and play with you. I have many of these stories if your interested. I took my son and his friend(14 years of age) several times to australia. Some very funny stories.(being played by monitors)
Also, I have seen very fast local lizards, play with our captive monitors. That had to be called playing of some sort. They would run up within inches of the monitor, bob their heads and zoom away at rocket speed and do it over and over. A deadly game of cat and mouse. Unfortunately the monitors won, as they simply waited until the fast lizards holed up, then dug them up. Cheaters I say. Cheers