Experiments demonstrating irreligious people spontaneously developing superstitious rituals?
Short answer
In accordance with @ArnonWeinberg's comment, I think superstition is the term you are after. 

Background
Superstition (e.g., Skinner (1948)) is:


  [A]ny belief or practice that is considered irrational[.] [F]or example [ a belief that] arises from ignorance, a misunderstanding of science or causality, a positive belief in fate or magic, or fear of that which is unknown. "Superstition" also refers to religious beliefs or actions arising from irrationality. 


I may, in fact, have found a video fragment of the one you are looking for, using @ArnonWeinberg 's clue in the comments. I searched for 

Skinner+Superstition+experiment+In+Humans+Video

And found this this awesome video. I had a good laugh, thanks! Pigeons, a bowl of fish, and a group of funny people trying to find meaning in chaos. 

Reference
- Skinner, J Exp Psychol (1948), 38(2): 168-72