When are semi-colons used in Chinese?
It is less common, but you will find semicolons used every once in while in Chinese text. The way of using it in Chinese is similar to English, where a comma is not enough but a period is too divisive. 

A good example is 开心，就开怀大笑；伤心，就掩脸痛哭。
A comma in between 大笑 and 伤心 would be odd, and a period would fail to show  that the two phrases are related.

The semicolons work for the excerpt from Press-Ganging Able-Bodied Men, because it separates the three steps of how the person would 替你办事. An alternative would be to write out 第一、第二、第三, but then it would be less concise and fluid.