This page details prerelease information and/or media for Doom (2016).
Doom 4 was intended to be, well, the fourth game in the Doom series. However, it was ultimately scrapped by Bethesda and id Software for feeling more like Call of Duty rather than Doom. In fact, Doom 4 simply became DOOM and was released in 2016.
The premise of Doom 4 can be interpreted as a reimagining of Doom II: Hell on Earth (1994), like how Doom 3 was essentially a reimagining of the original Doom released in 1993. Where Doom 3 focused on the UAC opening a portal to Hell, it's likely that Doom 4 was to focus on the aftermath, with the demons reaching Earth. It's possible Doom 4 was intended to be more action-focused, since Doom 3 was supposed to be horror.
Judging from trailers and a scrapped music track being titled The Resistance, Doom 4 likely centered around a group simply titled the Resistance, with the ultimate goal of eradicating the demons and reclaiming the Earth.
The Glory Kill system was kept in the final release, and this clip from the Noclip documentary DOOM Resurrected shows a proof-of-concept cinematic. Interestingly, the Combat Shotgun and Super Shotgun seem to have retained their models throughout development, but with the textures being different and the animations not even close to resembling the final product; Doomguy reloads the Super Shotgun one shell at a time (this is included in the final release, but as a rare animation), and he moves the Combat Shotgun to his left to pump it, similar to the animation in the original Doom titles in the 1990s.
Some Glory Kills include Doomguy shooting at what looks to be an imp until it gets impaled on a spike, using a pistol as a club to smack a demon onto a car and smashing its head against the hood, and just using the Combat Shotgun as a club.
It would appear that Doom 4 was to have regenerating health as well, which may have contributed to the "Call of Doom" reason for the game being cancelled.