None of descriptions describe it this way, but it seems likely that their "wave spring" adjusts the resonance frequency of the system. They talk about getting vertical motion 3x the wave amplitude under normal conditions, so it must be something like that. Because it is on resonance, there are already big differences in the forces (during parts of each cycle) on the anchor under normal wave conditions than you would expect from buoyancy during wave motion.
I don't think they are applying breaking forces during a storm, they are adjusting the system to be off-resonance to the wave to minimize motion. There will be large forces on the anchor during a storm, but that seems like it would be one of the primary design parameters.
The closest mechanical analog (but not a great one) I can think of is paddle ball (a rubber ball attached to a wooden paddle with a rubber band). Off resonance the ball flops around randomly, and on resonance it has a very large amplitude.