The article doesn't describe a stack. The closest thing is progressive bitwise OR operations on a ring buffer, good until your whole ring buffer is filled with 1s.
Assuming a typical audio encoding, each time around the loop the new sample value is added (arithmetic add) to the previous value, not bitwise OR. The mean value of a sample is zero, so you can do this forever. (Idealized. In practice you actively normalize to avoid overflow/clipping).
This does seem like a better analogy. The visual display on this particular loop pedal is a ring, as well. I'm going to think more about this!