Mike Stone gives us a quiet scene in two short parts: autumn leaves skittering past, and two men bent over a chess game. The speaker doesn't tell us what to feel. He just reports what he sees, and the details do the work.
The leaves are "brittle" and "unsatisfied," a strange word for leaves, as if they're restless and still wanting something. The men, meanwhile, are reduced to "two worn overcoats," so they seem as faded and weathered as the season. In the second part, a cigar stub sits in a coffee mug and a waiter folds napkins, which suggests a café where little is happening and nobody is in a hurry. By the end they are simply "two old chess players."
The mood is still, slightly melancholy, and a little affectionate. The title's pun on "checkmates" also hints at companions, not only opponents, so the game may matter less than the habit of sitting together as time runs down.