Born in Dunaszerdahely, Austria-Hungary, Steiner came to New York City at a young age. For a time, he was active as a boxer. At age 16 he was a member of the Hungarian Chess Club and the Stuyvesant Chess Club. With the experience he gained in the active New York City chess scene, Steiner rapidly developed his chess skill and in 1929 he tied for first place in the New York State championship tournament at Buffalo. The same year he was first in the Premier Reserves at Hastings, England. Steiner left New York for the West, settling in Los Angeles in 1932. He became chess editor of the Los Angeles Times that year, writing a chess column until his death. He formed the Steiner Chess Club, later called the Hollywood Chess Group, headquartered in a clubhouse next to the Steiner residence. The Hollywood Chess Group was visited by many movie stars including Humphrey Bogart, Lauren Bacall, Charles Boyer, and José Ferrer. Steiner and the Hollywood Chess Group organized the Pan-American International Tournament in 1945 and the Second Pan-American Chess Congress in 1954. Steiner played three challenge matches against Reuben Fine, one of the world's top players. Fine won all three matches: by 5½–4½ at New York 1932, by 3½–½ at Washington, D.C. 1944, and by 5–1 at Los Angeles 1947. One of his major international wins was at the 1946 London Victory Invitational, the first significant European tournament held after the end of World War II. Steiner challenged Arnold Denker in 1946 to a match for the United States Chess Championship at Los Angeles, but lost 6–4. In 1948 Steiner won the United States Chess Championship at South Fallsburg, New York, ahead of Isaac Kashdan. Steiner was a member of the United States Chess Federation's teams sent abroad to the Chess Olympiads in The Hague 1928, Hamburg 1930, Prague 1931 and Dubrovnik 1950. As reigning U.S. champion he captained the 1950 team. In the historic 1945 USA–USSR radio match between teams from the US and the USSR, Steiner was the only U.S. player to achieve a plus score. Although the American team including Reuben Fine, Samuel Reshevsky, Arnold Denker, and Isaac Kashdan, was badly beaten, Steiner scored 1½–½ against Igor Bondarevsky. Steiner was very active as a player in West Coast tournaments, winning the only two California Open tournaments he entered in 1954 and 1955, and winning the California State Championship in 1953 and 1954. He was defending his State Championship in Los Angeles in 1955, when after finishing his fifth-round game he felt unwell and his afternoon game was postponed. About 2 hours later around 9:30 pm, Steiner died practically instantaneously of a massive coronary occlusion while being attended by a physician. By agreement of the players, the 1955 California State Championship tournament was canceled.