Doom's multiplayer is now back under the guidance of id Software, and MP specialists Certain Affinity have been moved on. The studio, which has in the past worked on online titles including games in the Halo series, is no longer supporting Doom's PvP element; that is now being handled directly by id, with assistance from the BattleCry team.
The news emerged during our interview with id's Marty Stratton during Quakecon this week (you'll be able to watch that in full here on Gamereactor soon), at which point we were told about the studio's ongoing plans to support and develop the online side of the demonic shooter.
Late last year IGN reported that Bethesda weren't happy with the direction that the game was taking and that the BattleCry team were also working on other projects, but it still begs the question of whether the online title is even still in development. It has, after all, been very quiet on that front in the last few months. We've reached out to Bethesda for clarification and will update you once we've heard back.