How can we describe Joyce as a short story writer through examining "Eveline" and "Araby"?
This is something that can be done through an analysis of the way in which Joyce uses epiphanies in his short stories. Both of the stories you have indicated are excellent examples of this. An epiphany is defined as a moment of sudden insight or knowledge where a character is able to understand something about themselves or see themselves for who they really are. Normally, epiphanies occur towards the end of texts, and they certainly do in these two short stories.
For example, in "Eveline," the epiphany comes when the eponymous character realises she is unable to leave her home with Frank and take up the opportunity she has to escape. When the bell is sounded to board the boat, notice what she feels and experiences:
All the seas of the world tumbled about her heart. He was drawing her into them: he would drown her. She gripped with both hands at the iron railing... No! No! No! It was impossible. Her hands clutched the iron in frenzy. Amid the seas she sent a cry of anguish!
Just as Eveline at the end of the story realises that she is incapable of leaving Ireland and her domestic situation and responsibilities, so the anonymous narrator in "Araby" at the end of the story sees himself as "a creature derided by vanity" as he realises that he is not, in fact, some knight fulfilling a romantic quest for his lady, but just a young boy whose romantic notions have got the better for him.
The epiphany therefore is an important aspect of the writing style of Joyce and is definitely worthy of some analysis. I have included links below to the enotes study guide section of both stories, so hopefully they will help you to analyse the epiphany further.