I was at the Police station in Japan getting a driver's license today, so I asked about riding a OneWheel in Tokyo.
They said it's ok to ride in parks (any park, not just skate parks) but it's not ok to ride on the road. I asked specifically about sidewalks and bike lanes and roads, and they said ダメですよ (it's not allowed).
I asked them about the Solowheel too, since it's more unicycle like than skateboard like. They said it's the same.
Apparently, this has nothing to do with being a skateboard. There simply is no rule for these new devices yet, thus they are not allowed.
It's not a bicycle, thus not allowed in bike lanes. It's not a pedestrian, this not allowed on sidewalks. It's not a car or scooter, thus not allowed on the road. You get the idea :)
I tried "it's like an electric unicycle, and unicycles are like bicycles". But that doesn't work in Japan. Only bicycles are bicycles. And obviously electric bicycles are bicycles - hence the name.
I could think of more angles and questions, but it was becoming increasingly obvious that the officer was not nearly as interested as I was in persuing the conversation. In Japan, you have to learn when to simply bow, say "arigatou gozaimasu", and walk away politely... then ride anyway and feign ignorance :-)