Should the حدd penalty be carried out against someone who intentionally killed a married fornicator?

If someone kills a married fornicator, and establishes the legal proof of their fornication (either through their valid confession or the testimony of four righteous witnesses), then the killer is not liable for blood money, qisas (retaliation in kind), or expiation. However, they are sinful for overstepping the authority of the ruler and must be disciplined (ta'zir). But if they do not establish legal proof, then the punishment of qisas is applied to them, unless the guardians of the victim pardon them. They must also repent and seek forgiveness, because the implementation of legal punishments is the right of the ruler, not individuals.