If it weren't for the fact that all of "Cyclops" is told from his perspective, the anonymous narrator would just be another guy at the bar – another Joe Hynes, John Wyse Nolan, Bob Doran, or Alf Bergan. In terms of the action of the episode, he is only minorly involved, but as readers, we are forced to read the entire episode filtered through his point of view. Because he turns out to be a mean-spirited bigot, the fact that we get his handle on events can be a bit maddening, which is precisely the point.
Richard Ellmann, Joyce's biographer, has suggested that Joyce privately identified the anonymous narrator of this episode with Thersites, a deformed man who appears in the Iliad and was the loudest and most obnoxious talker among the Greeks. Throughout "Cyclops," we hear the narrator take digs at Bloom and think of how pathetic Bob Doran is for being a drunk. He seems a petty and judgmental man, much more ready to see the faults in others than those in himself.
The style of the episode can seem claustrophobic as we get stuck in the head of such a small-minded man. The narrator is used to demonstrate just how confining and "one-eyed" (because the narrator is also a double for Polyphemus, the Cyclops) it can be to write from the first-person perspective. The entire idea of a first-person "I" can seem myopic if that first-person is not capable of empathizing with others, of stepping outside of himself and at least trying to see things from other people's points of view. The writer of Ulysses himself seems to feel the need to break from the narrator's perspective. Thus the entire episode is interspersed with passages of parody that couldn't possibly come from the narrator's mind.