If you look at the first page in 2014, the time of the article, you'll find this: https://en.wikipedia.org/w/index.php?title=Arithmetic_deriva...
> E. J. Barbeau was most likely the first person to formalize this definition.
This suggests to me that Shelly's earlier definition in 1911 was not generally known. Indeed, Wikipedia has been a significant driver in rescuing earlier results in mathematics from obscurity.
But you can't cite what you don't know. So I wouldn't expect an emeritus professor, or anyone, to have either a time machine or a crystal ball.