Because I am rather old, I have thought a lot about this. I have seen plenty of info about the Deathmatch games and all pointed to the first Doom (1993) to be the "creator" of this type of game genre.
But in my mind was planted images of a comic, Strontium Dog of Ezquerra with Alan Grant's script, Ezquerra was also author of the Juzge Dredd character, on "Carnage" I did read a history called "Carnage" or "Matanza" in spanish. There you can see ALL elements of modern deathmach games, bizarre characters ,special weapons, the first healthkit, the final prize, the special weapon, a limited space where you must fight on, RULES, ALL we actually know about was there... in 1987, six years before what is claimed the father of the genre.
I encourage you to read it, so you can see it with your own eyes. I don't know if there's someghing similar out there, the most similar thing I have read was on Jack Vance's 1969 novel "The Dirdir", but the story, if you read it, is more a history with the presence of Predators, even some aspects of the Dirdir aliens was exact as the 1987's Yautjas.
In justice, I think Ezquerra and Grant deserves the fatherhood of the Deathmach games.