Bethesda are making big changes as Doom Eternal is apparently stepping away from traditional multiplayer modes that include Deathmatch which is quite ironic since the name is usually attributed to one of the original Doom's co-creators.
Doom Eternal is going to be primarily a singleplayer experience and while it will indeed have multiplayer, it will not be the standard things we got used to. In an interview with IGN, Marty Stratton the executive producer stated that the studio's lessons from 2016's Doom led them to make this decision.
As you probably remember, the 2016 reboot was wildly successful but those who praise the game mostly refer to the singleplayer power fantasy where the player is ripping Hell a new one. This is the thought that drove id Software to ditch the traditional multiplayer in favour of something new.
This "something new" refers to Battlemode that features three players in an arena. One player assumes the role of Doomslayer while the other two play as demons.
The traditional multiplayer modes usually include Deathmatch so dropping them also means no free for all killing fest and now it's replaced by a somewhat structured killing fest. On the bright side, the mode preserves that Doomslayer versus demons feeling.
It is kind of ironic that Doom Eternal will ditch Deathmatch since John Romero, a co-founder of id Software and co-creator of the original game is credited for coining "deathmatch" as a term to describe the game mode.
However, Doom games have always been viewed as singleplayer experiences, including the ones Romero worked on, so Bethesda aren't really making a transgression by dropping Deathmatch.
Depending on how good and how long the main singleplayer campaign turns out to be, it is highly likely that multiplayer will not affect the players' impression of Doom Eternal. On the other hand, if it turns out to be an interesting mode, it could potentially boost those coveted Metacritic ratings.