The photograph is later than 1915, when Duchamp moved to the U.S. to avoid World War I, and met Ray; it is probably after 1918.
The two even played chess in a movie:
Man Ray directed a number of influential avant-garde short films, known as Cinéma Pur, such as Le Retour à la Raison (2 mins, 1923); Emak-Bakia (16 mins, 1926); L’Étoile de Mer (15 mins, 1928); and Les Mystères du Château de Dé (20 mins, 1929). Man Ray also assisted Marcel Duchamp with his film Anemic Cinema (1926) and Fernand Léger with his film Ballet Mécanique (1924). Man Ray also appeared in René Clair‘s film Entr’acte (1924), in a brief scene playing chess with Duchamp.
The photo above is a still from that 1924 René Clair movie — it comes about 4:30 into the movie (the version shown here is half of the 20-minute movie, with a very modern, surrealist music score added; you can see the entire movie from Pathé, with a more contemporary score, here).
Update, March 14, 2011: See also this story from 2008 about Duchamp’s need to play chess, featuring of photo of Duchamp, Teeny Duchamp and the composer John Cage deeply engrossed in a game. A good read about chess, and Duchamp.