Chess is all about attempting to gain power over the board and over your opponent, therefore Eliot might be interested in chess as an allegory for sex and sexual violence because in the stories and myths that he references there is always an evident power imbalance (Ophelia, Philomela, Dido) where one sexual partner, most often the woman, must be subjugated. In other words, sex here is most often portrayed as a power play/battle for dominance. In a series of calculated moves the women are conquered and strategically ruined, as one strives to do to their opponent during a game of chess.

alludes to Middleton's A Game at Chess and Women Beware Women, which is quoted here in line 138: "Pressing lidless eyes and waiting for a knock upon the door". The character responding has so far been rather preoccupied by thoughts of death ("pearls that were his eyes", "Where the dead men lost their bones"). The closing of eyes is a common action used to prepare the bodies of people who die with their eyes open, hence this line might suggest that in our waking lives we occupy ourselves with fickle pursuits such as games of chess (which we know to be an allegory for sex) to distract us from the often daunting reality that we are all merely living in preparation for death, i.e "waiting for a knock upon the door".

Here is the connection to The Fisher King which I was referencing in my title annotation. Weston analyzes this king Arthur legend, among others, in her book.

Post-WWI Europe was completely ravaged, so this is a pretty self-explanatory allegory on Eliot's part. Later in "The Burial of The Dead" Eliot discusses his association of The Man with Three Staves tarot card to the Fisher King myth. The title of this poem may therefore also be alluding to the collapse of society due to the Fisher King's inability to reproduce, maybe because post-WWI life looked so bleak that reproduction seemed futile?