In Hungarian, a is the definite article, so it wouldn't be "a boy" with the indefinite article. "That is a boy." would be Az egy fiú. with egy (and with a full stop at the end and a capital letter at the beginning since it is a sentence).
Here we have just az a fiú which means "that boy" in English -- just a noun phrase.
Hungarian uses the definite article together with "this" and "that" -- so word-for-word it is "that the boy", but we don't say it like that in English.