You can have regerative braking on a non-electric car. There are two ways it can work.
1: The regenerative braking uses electric motor(s) attached to either the gearbox or the front wheels and they act as a generator under braking providing resistance and then putting that stored energy backinto the system under acceleration though the same electric motors.
2: A heavy (dense metal usually a type of swarf material) is connected to the wheels and engaged/disengaged through a clutch to slow the wheels under braking. This spins up the flywheel under braking when the clutch is engaged, transferring the forward kinetic energy of the car to rotational kinetic energy of the flywheel. When the car accelerates the clutch re-engaes transferring the energy back into the system.
They both have draw backs.
System 1 has a large component weight, complexity and packaging issues.
System 2 also has weight issues, of the flywheel primarily and complexity of the clutch mechanism. There is also the issue of the rotational energy of the flywheel having a gyroscopic effect on the car making changes of direction more difficult. This added to the extra energy actually required to carry it around in the first place.
The new rule in F1 which allows regenerative braking has most likely prompted Ferrari to look at it for general use. Ferrari historically is usually the first to bring F1 tech to the road.