No you don't need an another programm to play them. The files should be OK. The Finder is just to stupid to recognise them as MP3s and everything on this god damn OS depends on the Finder.

As far as I can remember is the "PC Extensions" control panel responsible for the filename extension <-> type/creator association. You can maybe use it to enforce that files with a .mp3 extension should be opened with application XY...

Oh, and here's iTunes 2.0.4 for Mac OS 9.x.x.

http://docs.info.apple.com/article.html?artnum=120073