A contract dispute I am currently in has a binding arbitration clause signed by both parties in Arizona, however, the other party filed suit and stated the case is not subject to binding arbitration.

Do I proceed with a Motion to Dismiss based on subject matter jurisdiction?

In general, if the party to a contract with binding arbitration clause is the party BREACHING the contract (allegedly) then the arbitration clause is sometimes rendered moot ... however wise litigants will search the case law to see how your local jurisdiction deals with such matters. Hope this helps a bit.