There seems to be a category of "archaeologist" that likes to explain artifacts they don't understand as being ceremonial or religious, because they can't think of any other explanation, and without having any information about what the ceremony is, or how the religion is supposed to work.
I take such claims to mean simply "We have no idea what this artifact is for; it might as well be something magical, for all we know".
You may enjoy Motel of the Mysteries by David Macaulay which pokes fun at what you’ve mentioned.
>”It is the year 4022; all of the ancient country of Usa has been buried under many feet of detritus from a catastrophe that occurred back in 1985. Imagine, then, the excitement that Howard Carson, an amateur archeologist at best, experienced when in crossing the perimeter of an abandoned excavation site he felt the ground give way beneath him and found himself at the bottom of a shaft, which, judging from the DO NOT DISTURB sign hanging from an archaic doorknob, was clearly the entrance to a still-sealed burial chamber.
Carson's incredible discoveries, including the remains of two bodies, one of then on a ceremonial bed facing an altar that appeared to be a means of communicating with the Gods and the other lying in a porcelain sarcophagus in the Inner Chamber, permitted him to piece together the whole fabric of that extraordinary civilization.”
I guess you are in some category yourself because you seemingly haven't read the large amount of literature about a global shamanistic culture, and archaeologically there is plenty of evidence that divination came before games.
Its natural, because games based on chance give us the feeling of being "hot" or "cold" ie able or unable to predict entropy.
MMI is a burgeoning science but if you're curious there is a group out there with access to QRNGs that practice influencing probabilities. And there is a small, but measurable effect size. And even not so small in some experiments I have personally seen, but being funded by Rockefellers means keeping your nose pointed away from the control grid.
I don't have a primary source, but have seen articles similar to these links that mentions the toy to religious object classification overlap (with almost the same pull quote):
I take such claims to mean simply "We have no idea what this artifact is for; it might as well be something magical, for all we know".