HSE 101
It’s not a DUI it’s an OWI. You can also get them: riding lawn mower, riding a bicycle, riding a scooter, riding a one wheel etc etc you get the point. This also varies state to state on what is and isn’t illegal. Where I live. Drinking and then riding a pedal bycicle willand you an OWI.
I live in a central European country and DUI laws here apply to operating a vehicle on public roads. A wheelchair or lawnmower isn’t a vehicle and on private property you are even allowed to drive a car drunk. A bicycle is a vehicle though.
Only in a motorized wheelchair, at least that is what people have been charged with. Could not find an example of manual wheelchair DUI, yet article says you can in any wheeled vehicle, such as a wheelchair or bike. One of several sources for confirmation, USA. https://www.findlaw.com/legalblogs/criminal-defense/yes-you-can-get-a-dui-in-a-wheelchair/
Note: and I would imagine these people had to be visibly, obviously and arguably endangering others, I wouldn’t expect to see a cop stop someone in a motorized wheelchair randomly just to test them and charge them.