An act is altruistic if it is costly for the acting individual and beneficial for someone else. Thus, punishment is altruistic if it is costly for the punisher and if the punished person's behavior changes such that others benefit. This definition does not require an altruistic motivation.
Think of queuing as an instructive example. Telling a queue jumper to stand in line is probably (psychologically) costly for the person confronting the queue jumper. If the queue jumper gets back into line, all people who were put at a disadvantage by the queue jumper benefit.
Scientific evidence for altruistic punishment comes from laboratory “public goods” experiments. In a typical public goods experiment, participants are randomly allocated to groups of four players. Each player is endowed with money units ...