This was obviously built by someone lacking even a basic understanding of how to use cryptographic primitives. It's not that hard to use an AEAD cipher construction properly. Nonce stands for number used once.
In linguistics, the term "nonce word" describes a term invented for a specific occasion/purpose where you have a need for a term that isn't met by existing language: https://en.m.wikipedia.org/wiki/Nonce_word
So the cryptographic term "nonce" was a reference to the existing linguistic terminology, which IIRC goes back pretty far, maybe into Old English.
I don't know exactly when/how the "number once" thing came about, but it's definitely become a valid definition in its own right... And a very useful mnemonic, as you pointed out.