You got it wrong.
firstly you say, that he left his brother in USA and travelled to Australia and settled in NSW, than you say in 1917 registered inMassachusetts for the war. BUT he was in Australia at the time, wasn't he?
In fact, His brother Petros migrated to Australia but from Greece, not USA. Fathers name BELLE should read BILL.
I guess, this is the brother
PETRAKOS aka PETERS; GIVEN NAMES - Peter; NATIONALITY - GREEK; PLACE OF BIRTH - Sparta, Laconia, GREECE; YEAR OF BIRTH – 15 August 1889; PLACE OF RESIDENCE - Kingsford, NSW; [Wife] PETERS, Christine Maria Martha