gyroscopic: in that there is a responsive, reflexive and restorative torque created when it is perturbed.
OK, agreed, but it all comes from the rapid spinning of the gyroscope!
Lots of things respond instantly and appropriately, and they don't need a freely spinning core. For instance the ground, or walls-- they always push back exactly enough to counteract what is put into them. Also a pendulum at rest has a restorative torque in response to perturbation (it pulls back to centered when you first touch it to start oscillation). Also elastic things like springs do this.. thus I feel yamabiko is a concept more related to ground reaction force, gravity-based pendulums, and soft, elastic (ju) tissues in the body. Or at least, moreso than to gyroscopes.