I don't think we should have capital punishment at all, anywhere, and certainly this is a textbook example of why, but circumstantial evidence is real evidence, admissible in court cases.
My understanding is that the opposite is closer to the truth: most cases are made on circumstantial evidence. Jury instructions apparently tell jurors not to weight it any differently than direct evidence.
Multiple witnesses seeing a suspect run out of a store holding a smoking gun shortly after the store clerk was shot is both circumstantial evidence and plenty for a DA to bring to trial.