According to the letter written by his lawyer, the salesman stated that all pre-existing orders will be honored. When a real merchant makes that kind of express warrantee between a clear buyer-seller relationship, it normally is enforceable. Though from what I've seen and been told, most courts will use whatever is in writing to be the final say, depending on the events that led up to the signing of the agreement or if the agreement in writing has been falsely misrepresented.
And yes, just because a background check was a conditional part of original agreement, does not rescind the contract. Both parties agreed that it will be conditional, as in, performance in passing a back ground check is required for him possessing the gun. If it was in a form of a counter offer, for example, a new condition added onto the sales agreement before the buyer agrees to the final terms of sale, then yes, it would not be enforceable.
The agreement was broken. The problem is, and always was, his remedy of breach of contract. Compensatory damages normally equal lost profits on the sale, not the difference between the contract price and market price. What he wants is Consequential Damages and Compensatory, and even punitive. To me, that is unreasonable, to say the least.