What power does the skateboard that children play now (the kind that moves up and down) rely on to move forward? Be specific!

This skateboard has two parts, each part has only one wheel and can rotate independently around the axis.

It depends on the inertial force of the object. When you slide forward, there is a forward force, which passes through your legs and is transferred to the skateboard, then to the wheels of the skateboard, and then the skateboard slides forward. If you want to keep sliding forward, you must have a constant force, which can be obtained by using your other pedal or using the inertia of your body.