I think your reading it correctly, but I would hope the law is more geared to recreational type devices such as scooters, bikes, etc., not adapted equipment such as a wheelchair or mobility scooter for disabled citizens. Plus, that law is dated 1967. They could try to uphold it but I doubt any judge would find it funny to see a disabled citizen being hauled into court for violation of a wheelchair or scooter.

Now, if you are doing wheelies in your scooter that's a whole other game.

I don't have advice for the ignorance of some people who park in the sidewalk. Here in Illinois that's a serious offense and you will be ticketed.