Yes, but those rules relate to riding the things. What we lack in this case is product safety legislation and standards. Presumably there is some for the hired scooters, but those are less likely to be taken on trains, and the private e-scooters are back to Victorian free-for-all.
If you start with regulations for riding the regulations then the current construction and use regulations for road vehicle can be amended to include e-scooters etc
Hire scooter main driver for their construction is possibly driven by the insurance provider the operator will have and the Local Authority granting the operating licence