Looking at the numbers on the graphs for single-slit diffraction, they are just binomial coefficient, at least mostly, not sure why there are pieces missing in the last rows. That is also what you expect when you repeatedly make binary decisions to go left or right. The article does not mention the binomial distributions once, it only appears in a comment.
And then they claim that it converge to the actual single-slit diffraction distribution, something with a Chebyshev polynomial and the sinc function, according to the article. Seemingly without justification besides looking at graphs and noting that they are both bell shaped. As said, not sure what is going on in the last rows of the graphs, but I would almost bet that the two functions are not the same, even in the limit as it becomes a Poisson distribution plus whatever the last rows do.
Why do they not just proof that the two are the same? The entire article seems to be about getting numbers out of their multiway system and then concluding that - if you squint hard enough - they look somewhat like diffraction patterns.