Bikes are not considered to be MOTOR vehicles anywhere.
In some states they are VEHICLES, but not MOTOR vehicles.
In other states they are "devices", but cyclists have the same rights as drivers of VEHICLES (again, not drivers of MOTOR VEHICLES).
It's called the DMV because it primarily deals with the regulation of Motor Vehicles. Part of that includes the licensing of drivers of MOTOR vehicles, which includes informing and testing drivers about the laws relevant to driving MOTOR vehicles, including those laws addressing the legal operation of VEHICLES and bikes (or including bikes, depending on the state) on the roadway.