The defendant is appealing a death sentence for the crime of child rape, not murder.
For most of man’s history, capital crimes included any "felonious" (i.e., serious) crime. As Charles Dickens observed, writing about the late 18th Century custom,
"[T]he hangman, ever busy and ever worse than useless, was in constant requisition; now, stringing up long rows of miscellaneous criminals; now, hanging a housebreaker on Saturday who had been taken on Tuesday; ... today the life of an atrocious murderer, and tomorrow of a wretched pilferer who had robbed a farmer’s boy of sixpence." ("A Tale Of Two Cities")
But after Caryl Chessman was executed in California in 1960 for multiple kidnap rape / robberies amidst public outcries, the Supremes ruled it a violation of the 8th Amendment to execute where no murder occurred. Chessman had been executed under a law enacted in the 1930's. California, like many other states, had made kidnaping itself a capital offense after the notoriety of the Lindbergh case.
A few years later, The US Supremes overturned a Georgia law permitting execution for rape of an adult (the victim was actually 16 years old) as "cruel and unusual punishment."
That has been the law in this country since. Now, as in the aftermath of the Lindbergh case, rage against abductors and molesters of children have led legislators in several states to reinstate the death penalty for such crimes.
Whether the Supreme Court, as presently constituted, will "honor precedent" as the recent nominees, Alito and Roberts, promised in their confirmation hearings, or will concur with their brethren Scalia and Thomas in a "strict interpretation" of the Constitution as it was intended in in the 18th Century is in serious doubt.