Brixton is a suburb of London where there were major riots in April 1981.
(These events coincided with the first Space Shuttle flight, which may
explain a lack of coverage in the US media.)

"Chess" has several levels of meaning. The chess game is used as a
metaphor for conflict in general. The riots were partly race riots (for
want of a better term), and "Chess" implicity refers to black and white in
opposition.  It also suggests a larger game beyond the knowledge of the
pawns - this refers to the political power play in the background.  An
inquiry into the riots partially blamed them on the economic policies of
Margaret Thatcher's Conservative government, which seemed to inflict the
poor with the economic cost of restructuring while leaving the more
affluent (the Conservatives' major supporters) relatively unscathed.

Which is all consistent with the themes of Fugazi.