Does playing tournament chess help one in the field of chess-related math? A question of personal interest.  Is "visualization" of various types of boards and graphs helped along by competitive, tournament play? Of course, I'm assuming play beyond simply knowing how the pieces move.
To the extent that "chess-related math" requires any expertise in chess beyond the rules(*), tournament play is probably not as useful as solving and composing chess problems/studies.  Typical positions in tournament play are too complicated to evaluate with mathematical certainty, while problems and studies should and usually do have rigorous proofs of correctness that are comprehensible to human players and problemists.

(*) Sometimes one needs no expertise beyond (say) how the Knight moves (as for questions involving the Knight's tour, or dominating the 8-by-8 board with a minimal number of Knights).