Fascinating. In Russian, the piece is still called "elephant" ("slon"), and in Slovene, it's a "hunter" ("lovec"), which I assume is connected with the old "archer" name. I did not know the word "alfin" and am surprised to learn that it was ever used in English, but it must have been, if the Century has a definition for it.
Just learned about this word through reading about the history of bishop and the bishop piece in chess. It looks like al-fin was the Arabic for elephant in which 'al' is the definite article like 'the' in English. The chess piece used to look like an elephant, then changed to archer then bishop.