"As long as man has been, and before man, there has been other species in space, struggling to overrule the other. One race, however, is not interested in it's power to rule, but instead it's lust to see who is deserving, or rather to spectate the elite veteran species in the games of the gladiators. The testing grounds are known as the Arenas."
The introduction of both Ranger and Grunt, in "Warriors of Slipgate". There's no Doom in here.
Also, the story of Sarge. In "Last Stand", Doom and Visor are talking about him in the resting area, while Sarge's regenerating. Cue flashback scenes about Sarge and Visor's previous fights in the Human-Strogg war.
Amulet of Concentrated Awesome: Ranger gives his teleporting amulet to Doom in "The Amulet", so he can use teleportation. He explains that it's done from the same technology the Vadrigar used for their teleporters.
An Axe to Grind: Ranger pulls out his axe in order to defeat Grunt in both parts of "Warriors of Slipgate".
Ascended Extra: Pretty much the entirety of the cast, which in the source, were just selectable characters for the player.
In "REBELLION!", Doom uses Ranger's rune in order to access the operations area of the Vadrigar. Then, he summons each one of the warriors. When they can't defeat the Vadrigar, Doom goes again to said room and summons Gorre, who takes care of the Vadrigar. Cue the Sequel Hook.
Chainsaw Good: Doom uses one in "Chosen By The Vadrigar". And, of course, there's the Gauntlet.
Lights Off, Somebody Dies: In the beginning of "Chosen By The Vadrigar", Doom is watching a movie, then the lights goes off and many of his companions bite the dust.
Mythology Gag: Considering the Idverse as a whole, there're plenty of these:
Some shots can be teleported and the jumppads can send the projectiles up, as a nod to Quake IV's multiplayer, which allows this.
The final part of Sarge's flashback in "Last Stand" is a throwback to the intro cutscene of Quake III: Arena, where Sarge is decimating thousands of monsters with his chaingun.
The aftermath of the match between Doom and Xaero in "REBELLION!" it's a throwback to the ending of the same game.
The amulet Ranger gives to Doom in "The Amulet" has the shape of the Quake logo.
At one point in "Chosen by the Vadrigar", Doom accesses a computer screen to see how many things came through the teleporter. Upon viewing the data for Phobos, the map screen that appears between levels in episode 1 of Doom shows up on the screen.
Neck Lift: Xaero in "DeFrag" and Gorre in "Worthy" both of them does this to Doom.
Nostalgia Level: "Chosen By The Vadrigar" takes place in a remixed version of the first map of Doom. Fans of the game may recognize many stages, aside of those which came with the game itself:
"Doom's Deathmatch Birth" takes place in Temple of Retribution. (q3dm7)
"No Backing Down" takes place in Proving Grounds. (q3tourney2)
"Warriors of Slipgate" (both parts) takes place in The Longest Yard. (q3dm17)
"Scrimmage" takes place in Wicked. (q3jdm8)
"REBELLION!" takes place in The Camping Grounds. (q3dm6)
Oh Crap: The first Cacodemon in "Chosen by the Vadrigar"'s green eye opens as far as it can upon hearing Doom revving the chainsaw. Hard to think a demon which is basically just a red ball of flesh would be capable of expressing this, but it does.
Wrestler in All of Us: Although the hand-to-hand combat seems out of place in a fanfic based on an old-school First-Person Shooter, there're plenty of moments where the warriors do throws and holds to their opponents.