"that apple" is az az alma in Hungarian -- demonstratives come with a definite article in Hungarian; that's just the way it is. Your feelings about how Hungarian ought to work don't come into it :)
And if it had been a sentence (with capital letter at the beginning and full stop at the end), then Az az alma. could mean "That is the apple" -- but as this was not a sentence but not a phrase, it's a bit more debatable whether "That is the apple" can be considered a correct translation.
From the written Hungarian -- no punctuation, no capital letter on the first word -- it is clear that the meaning must be 'that apple' and not 'that is the apple'.
But I wonder, if you were just hearing these words and not seeing them in writing, would there be slighly different intonations for the two different meanings?