Okay, so maybe there's some corruption on one of the install files. Clean it out to start anew. From xterm as root: (and for the love of god be careful with these recursive purge commands as root)

rm -Rf /home/user/.duke3d
rm -Rf /media/mmc1/share/duke3d/*
dpkg -r duke3d

Then re-download the .deb file and the .grp file.

Now reinstall:

dpkg -i duke3d_1.5.8-0maemo2_armel.deb

Move the newly downloaded duke3d.grp file to the /media/mmc1/share/duke3d directory and keep everything lowercase.

Try and launch the game.