The dealer said that he had just one word to say to him, he must either make his purchase or walk out of his shop.

In indirect speech, the reported clause's tense is changed according to the tense of the reporting verb. Here, the reporting verb is in past tense so the entire reported clause will be changed to past tense. "I" and "you" will both change to third persons. Here the speaker is using an imperative sentence so "must" is added.