The seems to have something that stops the end of it moving on until enough tension has built up to side underneath it. That much is fair enough. But then that same thing stopping the end would also prevent the same satisfying wiggle when it gets to the next position because it overshoots immediately.
The only thing I can think of is that the restraining pins move in and out is the clock have at just the right time but that would be quite a fiddly implementation and probably affect the visuals
As an aside, I'm not sure that doing this for the hour hand is a "good" idea. The difference between 10:00 am and 11:00 am is significant and needing to check how much the bend is doesn't "feel" right.
(late edit thought) If we're getting to the "this is controlled by some other system that doesn't need to be purely mechanical", having an electromagnet on at the right spot that then toggles off at one 5m increment and on at the next so that there's only one magnet active at a time could reduce possible issues of having the wiggle/snap attach to the wrong magnet.
It's possible that I've got the wrong mental model for how that would work.
Currently on exhibit at Chicago MCA - https://visit.mcachicago.org/exhibitions/gregory-bae/