Wikipedia says that this was identified in 1916 (New York Times, 12 March 1916) as an image of Ben Jonson (left; white) and William Shakespeare (right; black) playing chess. It seems that this claim that had been floating around in chess circles for a year or so, but most subsequent scholars seem to have considered this to be pure speculation. However, the claim was revived in 2004 by Jeffrey Netto, who argued that the chess game symbolises “the well known professional rivalry between these figures in terms of a battle of wits” (See Jeffrey Netto “Intertextuality and the Chess Motif: Shakespeare, Middleton, Greenaway” in Michele Marrapodi Shakespeare, Italy and Intertextuality (Manchester University Press, 2004) 218). As he puts it elsewhere:
This painting clearly evokes the theme of intellectual virtuosity. The two giants of British Renaissance literature are enmeshed in an intellectual contest that allegorically represents their well-known literary rivalry. Chess here iconographically depicts their battle of artistic wits, a battle before which the world can only marvel.
It looks as though Shakespeare is about to win the game, whatever about the artistic battle of wills.