Gasoline-powered, but no wheels...
Then I ran across a link.
They actually made gasoline-powered pogo-sticks that even grandpa can ride!
It's a single-cylinder engine, with the bouncing foot being connected directly to the piston, called the Hop Rod. There are a bunch of adverts and slightly more modern test-drives in a short video on the site.
Still, I wondered. Maybe the Hop Rod provided the inspiration for other wheel-less powered transports?
Do you remember those Russian boots? 4 metre strides and speeds of 40kph were promised, but that was 8 years ago. According to The New York Times they fell foul of Soviet secrecy and then Russian financial mis-management.
They're still around, waiting for some entrepreneur to hop on the band-wagon...