Hi Andy. Interesting question so I took some measurements.
Actuator play/lash=~.63 mm (used a dial caliper)
Tan, "Non-friction" pegs and cross axles used for all fulcrums and connect points in the lever mechanism.
As oriented in the video (straight up, level), Measurements at end of levers to a common baseline (unit in vise on my desk. Desk surface=baseline):
With actuator in the drive train:
bottom lever vertical movement at the end =7.5 mm, top lever=250 mm, lever1:lever2 ratio=33.3333
With actuator replaced with a beam the drive train:
bottom lever vertical movement at the end =4.0 mm, top lever=130 mm, lever1:lever2 ratio=32.5 (should be the same as other but close enough given measuring tolerance)
Difference between the two: 52%. So, it appears just that small amount of play in the actuator contributes to 52% of the total play of the lever mechanism. Well, probably not that much because even friction pegs (used in the beam that replaced the actuator for second set of measurements) have some play. Overall, the compound lever mechanism greatly amplifies motion and slop/play/lash (and force needed to move it I assume).