as well as characters of the pieces themselves (Knight Rupert of Schumann comes to mind), Bishops, the lowly pawn, etc. For a 23rd century version (more modern tonal language) consider Tri-Dimensional chess of Star Trek fame with its movable battle boards and vertical capabilities (Da - Daaaaa - da -da-da-da-daaaaaaaaaaa)
Indeed we would have to think of how to express Mr. Spock in music (he played that Tri-Dimensional chess, if I remember rightly)! But how would pure logic without any emotion sound?! Probably, that would be poor music, isn´t it?
(May be the so called "serial music" would express this mind adequately!
Seriously, to express the character or actions of certains chess figures could be a nice choice for composing "programme music" (german: Programmmusik), which (at least in german) is a term for music expressing non-musical matters. (F.ex. the theme "the noble Queen conquers the King" could be a good (and quite ambiguous) stuff, isn´t it?!