1. Place the archive somewhere on your N900.
2. Open the terminal and navigate to the directory where the archive resides (for example "cd /home/user/MyDocs" if you placed it in the main storage).
3. Extract the archive ("tar -xf omp_xxx.tar.gz").
4a. Navigate to the extracted directory ("cd omp_xxx") and run the installer as root ("sudo sh install_mediaplayer.sh --desktop-file").
4b. If it doesn't work (I'm not sure if sudo is configured out of the box), try "root", then "cd /home/user/MyDocs/omp_xxx", and finally "sh install_mediaplayer.sh --desktop-file".
5. Installer tries to start the player automatically, so you should hopefully see the result right away.

I think I'm going to look into the what's needed for the implementation, but if turns out to be too much hassle, It'll probably have to wait. Moreover, I'm not sure where to put the icon, as I'd prefer not to clutter the interface excessively.

Today I did not have as much time as I'd like, but I managed to put together quite usable playlist editor. It's not available for the current playlist yet, but you can fiddle with it in the playlist browser. To do so, select a playlist and choose "Edit playlist" from the titlebar menu and rearrange the songs by simple drag-and-drop or remove with a longer press. To store the result of your efforts, choose "Save playlist" from the menu. If you save an imported playlist, it will be imported even deeper, to "Saved playlists". Editing can be cancelled simply by closing the window.

Among other changes, shuffling a playlist from the browser finally works and useless "Delete playlist" button has been removed from automatic playlists.