What is a Dichotomy?
In a machine learning context, a dichotomy is simply a split of a set into two mutually exclusive subsets whose union is the original set. The point being made in your quoted text is that for four points, a linear boundary can not form all possible dichotomies (i.e., it does not shatter the set). For example, if the four points are arranged on the corners of a square, a linear boundary can be used to create all possible dichotomies except it cannot produce a boundary that splits the two points lying along one diagonal from the other two points (and vice versa), as you indicated in your own answer.