There are two issues. If I try to run ut2004-bin under System directory of Unreal Tournament sound appears but background graphics does not show up and if I try to run ut2004-bin-linux-amd64 game works without any issue but sound does not come. I now realize how sound of a game is as important as the game itself. If you try ls under System directory of Unreal Tournament you will see three files.
$ ls *.so*
libSDL-1.2.so.0 libstdc++.so.5 openal.so
To make the application run with sound on a 64 bit, remove these files are replace them with corresponding files of 64 bit Linux.
In my computer I replaced as follows.
cp /usr/lib/libopenal.so.1.13.0 openal.so
cp /usr/lib/x86_64-linux-gnu/libstdc++.so.5 .
cp /usr/lib/libSDL-1.2.so.0.11.3 libSDL-1.2.so.0
If you have updated these files the version numbers might be different.
Now run ut2004-bin-linux-amd64