Aus dem Wiki-Link im OP

Frontier justice is extrajudicial punishment that is motivated by the nonexistence of law and order or dissatisfaction with justice.[1] The phrase can also be used to describe a prejudiced judge.[2] Lynching [1] and gunfighting are considered forms of frontier justice.[3]

Examples

United States

   March 20 to April 15, 1882: Wyatt Earp and Doc Holliday tracked and killed 4 cowboys said to be responsible for Morgan Earp's death, which would later become known as the Earp Vendetta Ride.[4]

   Late 1800s: A group of self-appointed lawmen called "stranglers" lynched around sixty horse and cattle rustlers along southwest North Dakota's Little Missouri River.[5] ...

Vigilantism is the general term.

If this takes place in the old Wild West, then you can call it frontier justice, because, obviously, you need a frontier for this kind of justice.

Ja, auch aburteilen:

...The word may often be found in an attributive role, as in the phrases “vigilante justice,” or “vigilante group.” In this slightly broadened sense it carries the suggestion of the enforcement of laws without regard to due process or the general rule of law.

https://definitions.uslegal.com/l/law-arbitrary/

An arbitrary law refers to law imposed by the mere will of the legislature. It is not founded in the nature of things. For example, the tariff law. The term arbitrary law is used in opposition to immutable law.