This unique hoist mechanism has by some reason been preserved back from the very old days.
Before the era of electricity and compressors, motion power was generated by the means of water-wheels. The rotating motion of the water-wheel was then transformed into a lateral movement that could be extended over miles of "rod paths". At the site of usage, the lateral movement was then easily turned back into a rotary motion if desited. It's a bit like the coupling rods of a steam engine, with the difference that the rods were very long and articulated.
The interesting things with the Bastnäs hoist (and its siblings) is that lateral movement is transformed into pulling. The hoist wire was put around the wooden drum and each time the incoming rod made a forward motion, the drum was rotated. As the rod returned back, a locking mechanism kept the drum steady. Probably it was all very slow, but it was considered a great improvement back then.