Yes, pgChess extension now allows you to play a chess game with Postgres Instance(computer). Thanks to authors. Installation is very simple with pgxnclient. pgChess extension supported with another extension called pg2podg.
Documentation Link:
https://github.com/gciolli/pgChess/blob/master/doc/

pgxnclient install pgchess
pgxnclient install pg2podg

After installing, just run CREATE EXTENSION commands
 
create extension pgchess;
create extension pg2podg;

Two types of play, (1) PC vs PC and (2) PC vs Human.
To play a new game of PC vs Human run below file (download source from the above link for the files) in unaligned format of psql terminal.

postgres=# \pset format unaligned
postgres=# \i /usr/local/src/pgchess/pgchess-0.1.7/test/sql/play/PG_v_Human.sql

For your move follow below syntax when prompted “Your Move ? “.

        -- For now, we use this syntax:
        --
        --   XXpYYz
        --
        -- where XX is the starting square, YY is the ending square, p
        -- is the piece and z is an optional square where the desired
        -- promotion is specified.

Enjoy….

–Raghav