This is incredible! After hearing about the MIT tinker toy optimal tic-tac-toe machine[1], I built a half-adder out of dominoes[2] around the same time period as that video and hadn't ever heard of anyone else messing with the concept.
This reminds me of an article written for the April (first) edition of Scientific American many years ago... 1988.
The key thing to look for is the word 'Apraphul' which is the name of the island this was 'discovered' in. The part of the text of the article can be seen at Google Books [1] (many of the articles are behind a paywall)... though finely digging enough, I found it in a forum with part of the article [2]. Still, searching on 'Apraphul Pully' can take you to a number of other interesting pages (including one discussing the article's system).
Not to detract from a very cool demonstration, but it appears that all of the energy comes from the "inputs" which have to overcome all of the frictional forces in the system. With semiconductor gates, each gate provide the energy required to drive the gates it is connected to which facilitates composition.
Yes, this system is also prone to 'fuzzy' states due do slight variances that would multiply quite a bit if used for a full computation. It'd be cool to see a rectifier for this system, which will guarantee a full 1 or 0 state given a marginal state, though I'm not entirely certain how you'd build one.
Mechanical engineers have been solving that problem in various ways for hundreds of years. The gate in a film projector(or camera), the steam valve block on many steam engines, even the gear selector drum assembly on a motorcycle gearbox - and the mechanical gubbins inside every lightswitch displays the sort of hysteresis you need. I bet a typical 1950's engineer would solve that problem for you in a dozen ways in 20 minutes. (these days I suspect many engineers today would reach for a microcontroller and a servomotor or solenoid...)
Extremely impressive. Almost tempting enough to try and build an adder, but I fear for anything larger than a few gates the concept starts to become clunky to implement (see the gates at the end of the video ..)
edit: btw I can recommend every engineer watches this BBC series "what do artists do all day". The thinking processes of artists share a lot more with engineering that I expected and I found all episodes absolutely fascinating.