The principle asks a single question, was the act that caused death rash or negligent. It is not concerned with whether the accused had a general right to protect his property, or whether he bore any personal grudge against the victim, those are separate issues from the character of the act itself.
X wired his boundary fence with a live high voltage current specifically to keep intruders out, but that fence ran along a public street where ordinary people, not just intruders, could and did come close enough to touch it. Deploying a potentially lethal current in a place where innocent passersby are foreseeably at risk is rash, the risk to people like Z who have no intention of trespassing was entirely predictable.
X's right to protect his home from intruders does not justify a method that endangers the general public on a street, and the absence of any enmity toward Z is irrelevant since the offence here turns on rashness, not on motive or on any targeted intention that would point toward murder instead.
So the correct answer is X has committed an offence of causing death by rash and negligent act.
Asking what fact would need to be different for each option to hold shows where the other three choices run into trouble.
Since the danger to ordinary passersby was already foreseeable and no targeted intent toward Z exists in the facts, the option resting on rashness and negligence is the one that needs no unstated fact.
Therefore, the correct answer is X has committed an offence of causing death by rash and negligent act.