Is there a better-understood word that means "culpatory"?

The act of attributing something to a cause, a sort of blame, is called ascription. See ascriptive defined by Merriam Webster

relating to, marked by, or involving ascription.

ascription: the act of referring to a supposed cause, source, or author.

Also see if retributive justice or corrective justice is what you are looking for.

MERRIAM WEBSTER defines them as:

justice concerned with punishing or rewarding an individual.

Criminal justice systems can be considered as adversarial or inquisitorial.

In an adversarial system the prosecution attempt to prove the accused person is guilty and, usually, try to portray him in the worst possible light. The police investigation may aim at producing evidence to support the prosecution. The accused can defend himself, with or without assistance. The judge, and jury (if any), are neutral and have to decide between the prosecution and defence. Their decision is based solely on what the prosecution and defence tell them, plus the judge's technical knowledge of the law. Typically the jury decide on the fact of guilt or innocence, and the judge on the degree of culpability, if guilty.

The very poor 14-year-old boy, mentioned by the OP, was facing an adversarial system.

This is in contrast to an investigative, or inquisitorial, system where a judge, or investigating magistrate, is in charge of the investigation. He or she directs the police as to what aspects of the case to investigate and then aims to produce as complete a picture as possible. Sometimes this judge may then prevent his findings to another court.

The 14-year-old boy in question might have benefited from a more inquisitorial, less adversarial, approach to his case. There are, or course, arguments both ways.