Here's what that is about..
When they say non-detergent oil, they mean straight-weight (single viscosity oil) like SAE 30 etc - as opposed to standard multi-weight (detergent) automotive oil.
This is for two reasons. One, is that the automotive multi-weight oil is not designed to run in a gearcase. The action of the gears shears down the polymers in the oil, and will turn a 10W-30 oil into a 10W oil, in just a few hundred miles. The additives in modern multi-weight motorcycle oils fix this problem - so, they can be used.
- BUT -
There is another issue.. if the bike has been run for many miles with straight-weight (non-detergent) oils, it has probably built up oil sludge in the crankcase. Switching to a detergent oil after running without it, allows the sludge to break away from the parts, and clog the oiling system. On a moped, with an oil bath transmission, this is not that big of an issue.. but on engines with pressure fed oiling, it can lead to complete failure.
In any case, you are best off running with whatever the bike ran with in the past, as long as it was acceptable to the manufacturer.