That law defines safety requirements for low power electric assist bikes, and places their regulation under CPSC control, rather than NHTSA. It does not address licensing requirements, which are determined at the state level in the US (as I understand it - IANAL).
I had a long conversation with a man who described his son's ordeal after being cited for riding his electric bike without a driver's license and losing his case in court. Of course, that doesn't mean the story is true, or that the law is the same where you live. I would strongly suggest asking your lawyer for advice in this case. Disregard anything you read here - the stakes are too high.