The counter-rotating wheels are not the same as the two that the bicycle rolls on. So there's four wheels, two of which only exist to cancel the rotational inertia of the 'normal' wheels.
This. However I wonder what it would be like to ride a bike on two rolling-roads so that the front and back wheels moved in opposite directions. Or, indeed, a trike/quad with large coaxial wheel separation and contra-rotating rolling-roads.