This appears to be a misunderstanding. The box on the platform is for a battery, yes, but it was used to power an electric ignition coil:

The engine is geared to the wheel by means of a disk clutch. The flywheel, on the right side of the front wheel, contains a 6-volt lighting generator that originally furnished current for lighting and ignition, but the system later was altered by the addition of an ignition coil and four dry-cell batteries. The ignition switch is mounted on the right side of the frame, and the gasoline tank is above the front fender.

https://www.treehugger.com/autoped-was-worlds-first-scooter-4858489

There was no electric motor design in 1916 that could have powered this scooter from a battery that size.