Any amplifier with a resonance or Depth control of the type used by most guitar amplifier makers today are using the circuit developed by Fryette in the early 80s. And yes, it is effectively a means for adjusting damping factor around a particular frequency - in this case the speaker’s low frequency resonant peak as shown on a typical speaker impedance curve.
Damping is the control exerted on the speaker in an amplifier/speaker system and effectively limits the tendency of a speaker to “overshoot” or respond slowly to the application of electrical force.
Once you hit a speaker with low frequency electrical energy, the speaker returns to its rest state quickly or slowly depending on the damping action exerted by the amplifiers effective output impedance.
SS amps have lower effective output impedance by a factor of 10 compared to a tube amp, so negative feedback in a tube amp not only helps a tube amp maintain low distortion and decent linearity. At low frequencies where inertia and a large resonant peak team up to cause a speaker to wobble out of control, feedback is useful in lowering effective output impedance.
Fryette observed that being able to manually vary damping factor near the low frequency resonant peak of the speaker (thus the name “resonance” control) would be useful in “tuning” the interplay between the speaker and amp, allowing the player to dial in “tight” low end or “loose” cabinet response.
The contribution of cabinet construction to the behavior of the speakers and response of the amplifier, being a large variable between manufacturers using similar speakers, meant that you could use frequency selective variable damping to compensate for your amps behavior when used with different cabs.
More accurately, raising the effective output impedance around the frequency of interest to reduce damping factor around frequency of interest. In effect, variable attenuation of feedback around frequency of interest.