ZDoom

ZDoom came out during an age where space was still a premium - unlike today where we can buy 2+TB HDDs for 'cheap'. So people didn't really have a need to use MP3s at the time.

Edit: Also, forgot. People didn't have high speed internet like we do now. A 56k modem attempting to download a 10mb file was more akin to watching cement dry.

Download some old mods and check when it started. All I can tell you is that the first mod with non-MIDI music that I can remember is Torment And Torture 2, but that had a MOD, not MP3 or Ogg.

As soon as zdoom came out, an author would have done one in a matter of weeks? What about non-midis?