By my understanding, that window of gmplayer is present to serve as an XDND GUI interface, which of course needs to be visible before one could use it.
Using pure mplayer, windows are only created upon need and automatically torn down when no longer required.
xine-ui has an option
-H, --hide-video hide video window
and besides from that features a key binding editor.
I couldn't exclude such features might also be available in some mplayer GUI frontends.
If you are interested in a console GUI audio player, I could suggest looking into mp3blaster which is fully keyboard controlled.