A nameless narrator tells us of his own experiences in the red room firsthand. The first person narrative is actually indispensable for the story, since Wells’s main interest is exploring the psychology of the narrator. Telling the story first-personally allows him to reveal, bit by bit, the narrator’s transition from mild jumpiness to mindless terror. We also get to see the constant conflict between what the narrator tells himself, and what he’s actually feeling. The first person perspective also puts the reader herself in more direct contact with the narrator’s fear, making it easier to catch some of his state of mind.
Additionally, the first-person narration prevents the reader from ever knowing with certainty what’s really happening. There’s no omniscient presence to say, as the candles go out, that it’s really just the wind. Or, for that matter, there's no one to confirm the narrator’s diagnosis that the room is haunted by Fear. We never know whether or not there is a ghost. We have to take the narrator's word for it.