Not only in Eataly - 50cc combustion engined 2-wheelers are called mopeds here too. Their electric equivalents have somewhat inherited the tittle.
I don't know the Southern etymology, but around here this was a mixture of the earlier 'mopedi' (that's an easy one to guess...) and later 'mopo'. The latter is an appreviation of 'moottoripolkupyörä' = motorized bicycle.
Cleverly, this leaves the 'pedal or not' question on the background, giving less room for those annoying nitpickers who always jump up to swing their sword to cut the sprouts of a living language...not something to take place in this forum, of course