EAX sound is unsupported on modern systems. As the in-game implementation was quite buggy and caused crashes even on systems with EAX support, this is removed in the GOG.com version.
Install the DirectX End-User Runtimes.
Install the nGlide wrapper. Many users report this as an inferior solution to updated native drivers or DirectX, but if for whatever reason OpenGL doesn't work, this is an option.