This Easter Egg is located in the Gearhead Vault, within Subway Town. You can access it through a main story quest.
Once you're able to access this area, clear out all the enemies and head towards the area near the end with the computers. You'll need to activate 7 of them as shown in the video, and you'll hear a distinct sound effect from DOOM for every keyboard you interact with.
Once you've activated them all, head back to the beginning entrance, and a previously locked door will now be accessible. You will then find a teleporter that will transport you to a classic DOOM level. In that level, you will find a DOOM Marine Bobblehead.