Dorfman played in several USSR championships. In 1975, he took thirteenth in Yerevan (43rd URS-ch; Tigran Petrosian won). In 1976, he finished fifth in Moscow in the 44th Soviet championship as Anatoly Karpov won by a full point over Yuri Balashov. One of his most emphatic victories occurred in qualification for this championship, at the 1976 First League tournament, where he finished 1½ points clear of the field (+6 =11). In 1977, he was joint USSR Champion with Boris Gulko (both +4 =11, ahead of Petrosian, Polugaevsky and Tal). The subsequent play-off match was drawn (+1 –1 =4). In 1978, Dorfman shared thirteenth in Tbilisi as Tal won. In 1981, he tied for 8-9th in Frunze; Lev Psakhis and Garry Kasparov won). In 1984, he took 12th in Lvov (51st URS-ch; Andrei Sokolov won).
In international tournaments, Dorfman tied for second at Pécs 1976, finished second to Smyslov at São Paulo 1978, tied for second at Polanica Zdrój 1978, one-half point behind Mikhail Tseitlin, 1st-3rd at Djakarta 1979, 3rd-5th at Manila 1979. He won at Zamardi 1980. He was a winner at Warsaw 1983 (+6, =8), was 1st= at Lvov 1984, 1st at Moscow 1985, and 5th= at Minsk 1986.
He played for France in three Chess Olympiads.
- In 1998, at 2nd board in the 33rd Chess Olympiad in Elista (+3 –0 =6);
- In 2002, at 2nd board in the 35th Chess Olympiad in Bled (+1 –1 =8);
- In 2004, at 3rd board in the 36th Chess Olympiad in Calvià (+2 –0 =8).
He acted as one of Garry Kasparov's seconds in his first four World Championship matches against Anatoly Karpov. Later Dorfman moved to France. He coached the French player Étienne Bacrot from age nine to Grandmaster level, when he became France's and the world's youngest ever.
In 2004 Dorfman was awarded the title of FIDE Senior Trainer.
- Dorfman, Iossif (2001). The Method in Chess. Sarl Game Mind. ISBN 978-2957289028.
- Dorfman, Iossif (2002). The Critical Moment. Sarl Game Mind. ISBN 978-2847350029.
- Petar Velikov vs Josif D Dorfman, Palma de Mallorca (GMA) 1989, Zukertort Opening: Kingside Fianchetto (A04), 0-1
- Josif D Dorfman vs Yuri Razuvaev, Elenite 1992, English Opening: King's English Variation, General (A20), 1-0
- Championnats de France (French)
- Hooper, David and Whyld, Kenneth (1984). The Oxford Companion to Chess. Oxford University. ISBN 0-19-217540-8.
- Cafferty, Bernard and Mark Taimanov (1998). The Soviet Championships. Cadogan Chess. ISBN 1-85744-201-6.