You've pointed out the definition under the chapter regarding traffic control (316). However, under the chapter controlling drivers' licenses (322), the definitions of a motor vehicle is different.
§ 322.01. Definitions
(27) "Motor vehicle" means any self-propelled vehicle, including a motor vehicle combination, not operated upon rails or guideway, excluding vehicles moved solely by human power, motorized wheelchairs, and motorized bicycles as defined in s. 316.003.
§ 322.03. Drivers must be licensed; penalties
(1) Except as otherwise authorized in this chapter, a person may not drive any motor vehicle upon a highway in this state unless such person has a valid driver's license issued under this chapter.
Yes, your scooter does not qualify as a "motorcycle
", but all that means is that you don't have to get a motorcycle license. Because it is self-propelled, you have to have a drivers' license.
Sorry I don't have better news for you.