Atticusmj: I read on wiki page that one the copys of the game your able to save in is the gog that copy or one where can't save?
The main download link gives a very bare bones copy of Akalabeth; it starts with some garbage characters and then drops into pick your lucky number. No color, no sound.
In the bonus downloads are three items that don't have their titles set properly; they're listed as Product_Bonus_#####. If you download these they'll resolve as the Windows, Mac, and Linux installers for the 1998 version of Akalabeth, which is the official DOS port of the Apple II version which has color and MIDI music and the aforementioned save feature (though I wasn't able to figure out the hotkey to do so and the included manual is still the original manual).
My guess is the main game is the unofficial DOS port (it runs under DosBox).