Thanks for posting the video, interesting to see the innards! I have a little used Chiwanese chuck that has poor concentricity, might take a similar look at it in case there is muck deriving from manufacture causing a snag, though it may be just not very well machined and unimprovable!
I might take a precaution of dismantling individual components into some compartmented trays with a note of their location and pairings re the ( presumably numbered ) chuck jaws and slides, though.
( On the other hand, jumbling them might just result in improved concentricity, one never knows...! ) Dave