Interesting, Rakan has face blindness..... maybe? His sudden magical ability to see, recognize, and differentiate both Feng Shen and Mao Mao's faces kinda throws a wrench in that, but all his other symptoms fit.
@hansonagi 車 is the character used in Xiangqi to depict the "chariot" piece, which like the chapter pointed out would equate to the rook piece in western chess. It's commonly thought of as the strongest piece, since it lacks many restrictions and moves fairly freely, which might point to the idea that Rakan considers his uncle to be like that piece.
A reason he uses Go and Xiangqi pieces for different people is likely an indication of their "importance". As you may have noticed in the chapter, the number of pieces between a Xiangqi set and a Go set are vastly different; this is because Go does not put significance on each piece, while Xiangqi does. Thus, Rakan views "the vast majority" as Go pieces due to their abundance of numbers and lack of real significance to his personal life or work, using the black and white to differentiate the dichotomy of men and women. People who are directly related to his work or have significance to him would need further designation so he can move the right pieces unto the right places (Xiangqi is a military simulation, technically). Since every piece in Xiangqi has a role to play, it's as simple as assigning the appropriate piece to remind him what they're there for.