What does Trajan's response indicate about the important of the rule of law in Roman government?

You do not specify what you are referring to. I will assume that you are referring to the episode called the justice of Trajan where, while he was preparing for war, Trajan was petitioned for justice by the mother of a murdered man. He asked her to wait for him to return from the war, but she said he might not be back. Despite being busy, Trajan made time for adjudicating her case.

The story shows that in Rome issues had to be settled though the law and through a trial and that Trajan understood the importance of this. However, more than this, this story, which was told by Cassius Dio, was more about the character of Trajan, than the rule of law. He wrote: ""He did not, however, as might have been expected of a warlike man, pay any less attention to the civil administration nor did he dispense justice any the less; on the contrary, he conducted trials … and often elsewhere on a tribunal."