There was one earlier example of deathmatch as we know it, and I played it... after a fashion.
> MIDI Maze is a networked first-person shooter for the Atari ST developed by Xanth Software F/X and released in 1987 by Hybrid Arts. The game takes place in a maze of untextured walls. The world animates smoothly as the player turns, much like the earlier Wayout, instead of only permitting 90 degree changes of direction. It has been suggested that MIDI Maze introduced the concept of deathmatch combat.[1]
[snip]
> Up to 16 computers can be networked in a "MIDI Ring" by connecting one computer's MIDI-OUT port to the next computer's MIDI-IN port.
Hence the name. What a weird and wonderful hack.
On a personal note, I played a port of this... to the original Game Boy:
> A Game Boy version was developed by the original developers, Xanth Software F/X, and published in 1991 by Bulletproof Software (now Blue Planet Software), under the title Faceball 2000.[5] James Yee, owner of Xanth, had a vision to port the 520ST application to the Game Boy. George Miller was hired to re-write the AI-based drone logic, giving each drone a unique personality trait.[citation needed] It is notable for being the only Game Boy game to support 16 simultaneous players. It did so by connecting multiple copies of the Four Player Adapter to one another so that each additional adapter added another two players up to the maximum - seven such adapters were needed for a full 16 player experience.[citation needed]
Game Boy deathmatch. Never got to experience it myself, as my family only had the one Game Boy and we didn't know anyone else who had the game.