If the table were dropped on the arm, the antiskating knob would be bent or crushed. I can't account for the amount of play shown in the video, but if you were able to tighten the bearings a bit and they now behave, I can't help but wonder if someone previously tried to adjust the bearings and failed.
Put the level on the bearing (or measure from the plinth) to see if it is actually the bearings. If they are not parallel, I suspect you may have tightened the pivot pin into some location other than the actual bearing well - it happens since it isn't easy to see where the pin is setting itself - the proper place, or the notch between the pivot block and the lock pin or some other groove/slot. Surprisingly, at least for a while, the arm can appear to be pivoting with low friction. Until it is dislodge or jammed....
I think it more likely that the headshell is canted. Often the shell can be twisted slightly to adjust azimuth.
And use your eyes and a grid to look at the headshell when lowered onto a record. The up and down motion of the offset arm is actually an arc, not simply straight up and straight down, so the height at which you are checking the levelness may decieve you.