yes carl, i alluded to the tooling being old and out of tolerance (hah!) in my original post. unless they smash it with a titanium hammer between every run or do something incredibly ridiculous to it, i find this explanation to be nearly impossible.
however, think about the three objects in mechanical play in that video. there is a reinforced elastomer belt, an upper tooth profile molded in ABS and a lower tooth profile molded in ABS. the mechanical connection between the upper and lower tooth profile we can model as a cantilever with force equal to the elastic modulus of the abs that connects the two profiles.
now, elastomers stretch. the reinforcement laid into the elastomer is meant to control that tendency to elongate and to lower the elastic modulus of the elastomer material, but it can't eliminate it or else the belt either not be able to bend around the toothed gears or otherwise work as a timing belt connecting things with any degree of mechanical tolerance (ie, anything).
so anyway, the point is that if you're designing this abs part you don't design it so that it's "loose"; ie, within 3 sigma of mean you're slightly larger than the geometry of the belt, but you design it so that it's extremely tight (which jives with your experience carl), and so within 2-3 sigma of mean you're fitting a squished belt. now, imagine a belt that is a couple sigma thicker than the mean and a the cantilever detailed above. the action of the cantilever is such that the gap between the two tooth profiles could actually widen at the ends and lead to the the play that the video is showing.
hence, my advice, again, is to get a new belt (because your rig has stretched the crap out of your current one), and reinstall by moving the motor gradually to the right (looking from the front), then, once you have reached a point of maximum tension and the forces seem static (ie, the belt is not actively elongating), move to the carriage to the right endstop and fit the belt into the tooth profile at the rightmost point. at this point you should be able to get a feeling for what the play, if any is. use a very fine erasable pen mark or something if you want, make some prints, check for smudging, etc. your belt and profile play test is invalid because it neglects to factor in the rest of the mechanical system.
anyway, the x-y stage of the any printer of this style is going to have a huge number of error components everywhere, and doubly so if you use abs in load bearing parts. it's not anyone's fault, it's just physics.