In the SU the chess players enjoyed privileges unavailable to the general population, e.g., they could travel abroad (at least as long as they were winning, I read that Taimanov had his passport confiscated after losing to Fischer in the Candidates Match.) They also were favored at the higher education institutions, i.e., as a successful chess player you didn't have to study much to pass and get a degree.
As an aside, I heard from a guy who knew David Bronstein personally that Bronstein could have easily won the World Championship from Botvinnik in 1951, but it was made clear to him that it was considered undesirable for a Jewish player to beat Botvinnik. Bronstein according to my friend was a broken man after that, became excessively extravagant and never played with the same strength again.