A similar trick is done by Type II topoisomerases, which are molecular machines found in just about every living cell. Type II topoisomerases pass one piece of DNA through another. See https://en.wikipedia.org/wiki/Topoisomerase_II
Well, in fact the topoisomerase CUTS the second DNA and ligates it afterwards, so it is obvious it can pass through. I don't think it's similar at all.
Fun fact about Type II topoisomerase: even though it only has local information (the area where it acts) it manages to move in the correct direction (lower unknotting number) about 90% of the time. AFAIK, no-one knows how.
The spoke has been cut (by design) and the shaft passer sits at the cut, where the shaft passes through it. It cleverly does this "airlock-like" without falling apart and letting the two halves of the spoke separate. Similarly, the topoisomerase, after cutting the "spoke" DNA, becomes covalently bound to each side of the cut. Then the "shaft" DNA passes through the topoisomerase, without the topoisomerase falling apart or letting the two sides of the "spoke" DNA drift apart. Multiple "shaft" strands can pass before the "spoke" strand is religated and the enzyme detaches. So I think the principle is quite analogous.