Judging from the games the narrator plays in "Araby," how old do you think the narrator is?

The narrative point of view of this story is actually first person objective, and this means that the narrator is a participant in the story but that he is narrating it after the events have taken place.  You can typically identify this point of view by noting that the speaker uses the first person pronoun "I" and past tense verbs when narrating the story's action.  So, the narrator is actually an older person who is looking back and telling the story of what happened to him many years ago (his word choice in certain parts of the story alert us to the fact that he is much older now).  However, when the story's events were actually taking place, the narrator was of an age when he played outside with all his friends: running and hiding and pretending together.  This is a good clue that the narrator is perhaps in the 8-10 year old range.