He was educated at the Technical High School, Budapest, and gained a diploma in mechanical engineering (1926) from the Technikum Mittweida, Germany.
In 1923, he tied for 4-5th in Vienna.
In 1925 he took 2nd, behind Sándor Takács, in Budapest.
In 1935, he won (+3 –1) vs Henri Grob.
He played for Hungary in four Chess Olympiads:
In 1931, he played at second board at 4th Chess Olympiad in Prague (+10 –3 =4).
In 1933, he played at second board at 5th Chess Olympiad in Folkestone (+5 –4 =5).
In 1935, he played at first board at 6th Chess Olympiad in Warsaw (+7 –4 =7).
In 1936, he played at second board at 3rd unofficial Chess Olympiad in Munich (+13 –2 =5).He won individual bronze medal in Prague, and team gold medal and individual silver medal in Munich.Steiner emigrated to Australia in 1939.
He won the Australian Chess Championship four times in 1945, 1946/47, 1952/53, and 1958/59.
He also won nine of his ten attempts at the New South Wales title (1940–41, 1943, 1944, 1945–46, 1953, 1955, 1958).