While the videos show the barrel/gun movement, just because the barrel/gun is moving it does not mean that the dispersion will be increased. To produce an increase in dispersion will require a change in the barrel/gun movement from shot to shot or a change in the timing of the shot exit compared to the movement otherwise you will simply get a bias not an increase in dispersion. This is where some of the barrel harmonic theories fall down as the difference in the shot exit times is insufficient to attribute the increase in dispersion to the barrel harmonic movement. This inconsistency in explaining increased dispersions is what has given rise to the barrel pressure pulse theory as the pressure pulses will move up and down the barrel at a very high rate, much quicker than the projectile. If a pressure pulse reaches the end of the barrel at the same time as the projectile then there will be an increase in yaw rate on the projectile due to a change in the projectile barrel fit at that instant. If the times are different then there will not be any increase in yaw rate and the projectile will hit in a different place on the target. Because of the high speed of the pressure pulse effects, only a very small change in projectile exit time is needed to change from the times matching to not matching. I am not entirely convinced of the pressure pulse theory for airguns as the pressures are relatively low compared to fire arms.
A movement of 2 thou in the barrel end would only give an error at 50 yards of .2 inches. A C of G offset of 4 thou in the pellet will give a large initial yaw rate and over half an inch error at the same range and so will be more critical. This is because the basic design of pellets gives a poor response to initial yaw rates when it comes to dispersions. Barrel vibrations will also give an initial yaw rate but again we have to consider variations in the yaw rates, not the yaw rate values themselves. Barrel harmonic vibrations will tend to be more consistent in their period and direction thus giving more consistent yaw rates as opposed to pellet C of G offsets which will be in random directions.
Adding moderators etc. to the muzzle end will change considerable more than just the barrel harmonics. The intermediate ballistics will be changed which may well have much more effect on dispersion than any weight or damping effect on the barrel.