The Talmud explains that Phineas fulfilled the law כל הבועל ארמית קנאין פוגעין בו. One who engages in sexual immorality with a gentile woman allows a zealous Jew to perform a para-legal action and kill the perpetrator. However the גמרא qualifies this ruling that the decision has to be self-inspired. If however one comes to the Jewish court, בית דין to ask what to do they do not rule that he may kill the perpetrator. The zealot has to catch the perpetrator as he is committing the crime and if not the zealot is executed. זמרי also had the right to disengage and defend himself against פנחס who is considered a רודף because although he was allowed to kill זמרי he was not authorized by the court. However nobody other than זמרי could defend himself by killing פנחס which is not the case concerning one pursuing a murderer.
From the law here however it is difficult to understand how the Torah relates to a קנאי, a zealot. Hashem condoned and rewarded פנחס greatly for his action. He actually atoned for the sin of the people. On the one hand he is protected from retribution if he kills them in the act. However, if he does not manage to kill them in the act then he is a murderer and the victim is acting in self-defense killing his pursuer. Would stabbing a homosexual at a gay parade while not engaged in the sexual act or killing an Arab as retribution and hopefully preventing future attacks especially one disturbed at the government's generally weak response to Arab crimes carry the full penalty of murder without due process unless our situation can be defined as an ongoing state of war.
There is a similar הלכה in the Torah. The גואל הדם pursues one who killed a relative accidently. As long as he does not commit himself to the city of refuge the pursuer is not prosecuted for taking the law into his own hands. The difference between the two cases is that the גואל הדם has to be a relative. The zealot does not have to be a relative. However, it would seem that the הלכה is the same. We mitigate the crime based on ones feelings or religious conviction that does not allow restraint. In the case of the גואל הדם the victim can defend himself even though the pursuer is within the law. However in both of these cases the question remains. If the act is justified why does the court refrain from a green light to the zealot? His intent is to uproot evil from the midst of the Jewish people. Such heinous crimes especially done in public would have irreparable consequences if not punished! Therefore the question remains why does the court refrain from deciding? It must be that the court will not publicize the law because it is a slippery slope publicizing taking the law into one's own hand. This does not indicate however that they are opposed to the action. Secondly, how can the court sanction an action that contradicts what the court would decide for such a crime? This would cause the court to lose face. Here they are concerned with the consequences rather than the justice of the decision. Can a person like זמרי defend himself against a שליח ב"ד for חילול שבת? There is a difference between conduct rules and decision rules. The courts are required to exercise the rule of law to maintain law and order. This never takes away the right of the accused for self-defense. However there is a distinction. פנחס is still a personal vendetta although totally justified. It is out of the confines of the courts.
He is allowed to kill זמרי but not required.
We can conclude that the Torah protects a zealot from prosecution for murder but not however a justifiable defense (justification). Jewish law actually opposes the fanatical, because it is contrary to justice, and exempts him from punishment only in retrospect, probably for reasons of "understanding" the heart of a zealot who could not hold back in the face of sexual intercourse with a gentile in such a public manner. Phineas was wholehearted in his devotion to Hashem and could not tolerate the desecration of G-d's name. He received as a result an eternal blessing. However, similar responses although stemming from genuine feelings if not the products of wholehearted devotion to Hashem can be a heinous a crime as the perpetrators. We cannot in our generation resort to these methods since we are not aware of our true motivations. We must replace this with prayer and sincere fulfillment of the mitzvos of the Torah.