“Thou’ and ‘thee’ are archaic words used in the Biblical stories and in the times of Shakespeare. Whenever there is a sense of ancient times, addressing someone of higher rank, or something related to religion or divine elements, use of these archaic words makes sense.
 
Thus, Abou Ben Adhem using the pronouns ‘thou’ and ‘thee’ instead of ‘you’ while addressing the divine messenger, the angel is only befitting as a mark of respect.