In this type of game there are lots of collisions between the ball and flippers, spinners and so on. We need to be very clear about what assumptions we making for these type of collisions.
In any collision the linear momentum will be conserved for a closed system, but we have to be very clear about what is inside and what is outside of the closed system. It would be easy to miss out the linear impulse between the spinner axle and the base of the table. So in this case we cannot use the equations for collision response of free floating objects.
It might be tempting to use the equations for collision response of free floating objects but to increase the mass of the small spinner to make it linearly immovable but, that would give the wrong result, it is the axle bearings not the mass that should do that.