Absolutely agreed, our door is closed all the time whenever the aircraft is moved, and we would never use a device like this to move it. I just thought that it was pretty cool, I do however know of people that do not mind leaving the door open, and I can not imagine that if the door bumps into something the aircraft will never be able to pressurize again.Not being dramatic, seen it happen at a Signature. They never could fix the problem after it happened. If you prefer to leave the door open. Go right ahead.
Simply put, shutting the door prior to tugging could avoid a big head ache.
That is all.
The visual of a fueled Global or Gulfstream pushing that "toy" off the ramp and into the woods has me chuckling...