The chess match serves as a metaphor for Marlowe's interaction with Jesse Breeze.
Marlowe moves back and forth between his front room and kitchen as Breeze calmly
sits and intimidates him. It is like a chess piece moving back and forth to escape the
threat of a more powerful piece. At the end of their encounter, Breeze puts Marlowe in "check" by issuing an ultimatum that he must make a move by noon the next day or he will quite literally be "captured" by being arrested as a material witness.
The High Window