I had been trying Ubuntu, which had a graphical adventure game -- I believe it was Falcon's Eye. It seemed to work all right on Ubuntu. With the same hardware running Knoppix / Debian, the game can be called from the menu. It changes the pointer icon, flickers the screen once and then nothing else happens.

This is similar to the behavior of XBattle, which changes the pointer icon to indicate it's trying to open, and then does nothing else.