DMX was a sound library written by Paul Radek of Digital Expressions, Inc.  that was used in the Doom engine to provide sound and music playback under DOS. The use of this external library meant that when the Doom source code was later released, only the source code to the Linuxdoom port could be made public, as disclosure of the copyrighted DMX APIs could have resulted in an infringement lawsuit.
Various sources imply that the Id programmers were dissatisfied with the DMX library. John Romero was quoted in an alt.games.doom newsgroup post as having called Radek a "shithead", "Sound dork" and "incompetent" . Carmack later described the use of DMX as "a mistake" in the release notes to the Doom source code .
References to DMX can be found in Doom (although not in the game directly): a DMXOPTIONS environment variable allows various sound options to be set, and the DMXGUS lump contains instrument mapping data for use on the Gravis Ultrasound card.
Despite Id's unwillingness to release any DMX-related code, Raven took a much more relaxed attitude to the issue, and DMX-related code was included with the Heretic and Hexen source releases (although not the DMX library itself).