According to the official Doom video game Twitter account, the video game series' creators "Were not involved with the making of this movie." In several interviews, the director confirmed this but added that Bethesda & ID Software were asked to be involved in the production, even prior to a script being completed. They were asked to contribute to the story, script, casting & demon designs. They declined and wished the production good luck.
(at around 38 mins) The name of a dead scientist facing by the team is John Carmack, in honor of John Carmack, one of Doom (1993)'s co-creators. This also doubles as a reference to one of the scientist characters in the first film.
(at around 1 min) In the opening scenes it states UAC stands for United AeroSpace Corporation. In the Doom games UAC stands for Union AeroSpace Corporation.
(at around 30 mins) The first fallen UAC soldier encountered is named "William Blazkowicz". This is an obvious nod to the primary protagonist from id Software's other hugely popular game, Wolfenstein (2009).
Malcolm Betruger is a character from the game Doom 3 (2004) and like the character in the game, is the antagonist and the human working for the demons.