There are deep historic and esoteric meanings to the game of chess as well as it’s setup numerologically and spiritually.
Astrologically, the King represents the Sun and the Queen represents the Moon. The King who is limited to one square movements is like Shiva, the awareness and consciousness while the Queen is like Shakti, dynamically moving and commanding the energy.
The Bishop’s diagonal pattern of movement is taken to represent the spiritual world and represents the planet Jupiter. The Rook moves “on the square”, either vertically or horizontally. It is masculine and represents Saturn. The Knight is the only piece which can leap over other pieces. It represents the planet Mars. Pawns move straight forward one square at a time and are metaphors for spiritual advancement and reward. They represent Venus and Mercury.
Physically one could say, the kings represent the spirit, the queens the mind, the bishops the emotions, the knights the vitality, and the rooks the physical body.
There are correlations between the 64 Squares of the chess board and the 64 Hexagrams of the I-Ching. The 8 major trigrams of the I-Ching coincide with the 8 ranks and 8 files of the chess board, and the six lines in a hexagram may be correlated with the 6 types of chess pieces. There are also similarities between the chess pieces and the cards in a Tarot deck.
The game represents the White King and his legion of the Self against the Black King and his legion; the Not-Self, the void, the shadow. The King, like the spirit, cannot be captured or killed.