I think ESDF actually might be the more classic control scheme from the early FPS era. I'm not sure which came first but they both seem to have been common around that time, especially after the release of Quake. According to this quote attributed to someone named Jon A., the rise in popularity of WASD was somewhat arbitrary:
"Quake did not default to WASD. The default controls in quake were actually the arrow keys. The Quake community started using ESDF and WASD (as did Doom before Quake). However, the big push toward WASD happened when Thresh (Dennis Fong) won John Carmack's Ferrari in the first big Quake tournament. After that people started sending his Quake cfg file around and using his settings in hopes of being as good as him. He used WASD and the rest is history."
I don't have anything to say about this game we're commenting underneath in particular (and nothing against WASD as a choice), this just caught my interest. My dad is a Gen X gamer who loved Quake and Unreal and he always uses ESDF for movement so I had a feeling it was an older thing.