It was probably positive edge-level triggered (and debounced) without considering the second release event. It's a common failure of digital interfacing state machine design.
> To this day believe that the beep always came before the second click. I tried to trick it by clicking it once and only thinking about the second click — and the beep never came.
Yep. The shortcut is either to look for down-down or down-release-down, rather than down-release-down-release, but then the UX becomes inconsistent.
Debouncing refers to removing the dozens/hundreds of random momentary conduction events a real physical switch makes just prior to making contact on a human time-scale that are readily visible on an oscilloscope. Without debouncing, momentary switches would be unusable.