I don't know if this will work. It starts at about 0:32.
https://www.youtube.com/watch?v=dAsDeLP5Rao
I found the product by a Google image search. The pics below are from an eBay listing. It appears the scooter is also still sold on Amazon.
I noticed the picture of the platform with the blue-grey waterproof layer to sit on. You can see the little toggles around the edge where you attach the fabric drag bag to the platform. When attached, the wooden edge will be outside the drag bag. A close look at the photo on the box confirms that.
If the dog goes too fast and tips it as shown in the video, then the leading edge must be scraping the tile. Not good for your floor. He doesn't care, but if he went on carpet and tipped it like that so it he was dragging the edge, then he'd be pulling extra hard with the wooden edge fighting the pile of the carpet. He'd be pulling harder than if he had a standard (no wheels) drag bag, or if he had simply nothing at all. That would increase the work of the dog instead of decreasing it, and cause additional neck and shoulder strain.
However, the young dog in the video running down the linoleum hallway is having a blast, like a kid with his first bike!