I have aphantasia and I play chess (albeit not very well...)

Honestly, I think that aphantasia is a bit overhyped; I can do virtually all the things that people with normal mental imagery can do, except I suppose actually visualize the thing in my mind. The way that it works feels akin to a blind man groping in a dark room. If I try to visualize a chess board, of course I only "see" blackness (or nothing), but if you ask me what square is at e2, I can kind of mentally "feel" in that area and know that there's a king pawn there. And I can kind of "feel" below it that there's a king, and a queen, etc.

Normal people see things in their visual imagery by directing their attention at a spot in their mind, seeing it, and then registering what they saw. I just skip the middle step.