The main themes of "The Dead" are emotional paralysis and self-realization. Gabriel is a spiritually and emotionally "dead" man who does not realize it in the story until the end.
Gabriel is a disaffected man who is more concerned about impressing others and daydreaming about things he wants to do, but does not have the skills to do (emotionally). After attending a party, his wife breaks down and confesses that a song she heard there reminded her of a young man who desired to be with her that she rejected. The young man, after being rejected, said he had nothing to live for now. He apparently committed suicide afterwards. This moment is when Gabriel has his epiphany. He realizes that he could never love anyone like the young man, Michael, loved his wife Gretta. He realizes how totally disconnected he has been emotionally not only to his wife, but to all others in his life as well. He has been paralyzed by his own inability to empathize and feel for others. Through this epiphany, he experiences his enlightenment and self-realization.
This is similar to "Araby" in that the main character also has his own epiphany about his reactions to events in his life. The character comes to the realization that he has wasted lots of valuable time obsessing over an unattainable sister of a friend and that he has much to learn about real love and what that entails.