The Nightmare appears to consume victims by taking them through physical realms that encompass the victim's personal hells. In the case of Caleb, it took him through his memories back to his time in the arctic north (Episode two of Blood), and then through the memories of the other Chosen. In Ophelia's case, he was brought back to her entrance into the Cabal during a undead invasion in her college years. In the case of Ishmael, Caleb was brought back to his time as JoJo. In the case of Gabriella, she relived a stay in a haunted mansion. After Caleb drifts through these memories, he ends up in a Western ghost town (which may or may not be one of his memories, as it is not explicitly stated).
The Nightmare appears to be after Caleb solely, since after Caleb's sequence he is whisked away into the other Chosen's nightmares. It is unknown whether the Chosen are actually being torn away from reality and forced to relive their nightmares, whether Caleb is reliving it through their eyes, or the levels are simply a sort of flashback. Ishmael, Ophelia, and Gabriella don't appear to leave the campsite, and do not exercise any surprise when they return, nor do they acknowledge Caleb's presence in their memories, except within the memory itself.
The Nightmare succeeds in bringing Caleb to his realm through a portal in Westworld, at which point Caleb defeats him, and appears stuck in that land. This is the last point of canon continuity for Blood, and essentially, is where the story ends for the entire series (except for some nonsensical narration by Gideon).