What does 一个赛一个不讲理的 mean? Does the 的 determine its meaning?
赛 is the same as 比 in this case.

一个赛一个不讲理的
　　　↓
一个比一个不讲理的
　　　↓
一个比一个不讲理
　　　↓
One is more unreasonable than another is.

The word '的' is not important, and can be removed.