Data Scientist Prerequisites: What are the essential prerequisite statistics topics?
Everything on that list is is important material you should know. The sequence the topics are introduced looks to be chosen so that the material builds on itself as you move through (this effect is never totally perfect but seems generally right in this case), so I'd pretty much read the chapters as they appear.
The material listed is the most basic of basic statistics, so it is hard to make a case to omit something. 

However, while knowledge of these topics is important, it is very common (probably 'more common') for data scientists to involved in machine learning, which is a different approach to analysing data which gives better results for prediction. An overlapping term (not completely equivalent) term that is used is 'data mining' - searching on Amazon for these terms will give good results that can be used to pick a book that matches your background.

Note that statistics and machine learning are both heavily dependent on maths, especially calculus, linear algebra and probability. The book you mention has been written for people with little background in these, but to go deeper you'll need to brush up or get new knowledge in these areas.