1984 is the magic year in Ontario Canada when the government decided they would 'regulate' mopeds, snowmobiles and other "off-road vehicles". Before then it was basically just ride them and registering anything like a tractor, snowmobile, moped, minibike and such was either optional or local jurisdiction (I still have some of the bicycle license plates from my town) and even then it was more of a recommendation in case of theft then something which was enforced.
People deciding mopeds were somehow a DUI vehicle is urban legend and as true as calling a lawn tractor a DUI sedan. Up until the 1980s people in the main stream really did not take such a hard line against DWI/DUI. It was common place for local law enforcers to let Charlie drive himself home because it was too far to crawl or stumble if the 'knew' the person. The cops would just drive behind them or go check at their residence after to make sure the car was parked in the driveway.
Back then drunk at the wheel was seen more as an annoyance which some people could or couldnt handle, sort of the way people debate 'distracted driving' today.