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).
To paraphrase G. H. Hardy, while chess problems can be beautiful, they are trivial. The best and most difficult mathematics is "significant" mathematics, i.e. mathematics that helps you solve other problems and impacts other fields of math. So being good at chess probably won't help you much with math. Also, at least according to Hardy, chess is a primarily psychological game, as opposed to math which is purely logical (paraphrased from his Mathematician's Apology).
Consider this, what if playing tournament chess led to blindfold play? Then, along these lines, better blind play led one to visualize, even multi-task chess/math problems while doing routine tasks, like while driving for example. One would, at the least have more time to come up with new ideas! Did I mention I can do this?!