No. You do not have to own them. You can borrow them from a library or anybody else that may possess these books. Furthermore, all the other complementary documents can freely be downloaded from the internet.
However, the question you want to ask is probably not about possession but if you need to read or study the recommended textbooks. And the answer to this question is NO. The NPPE Candidate Guide clearly says that you do not necessarily have to use the recommended study materials and that you should get to master the topics of the exam the way that suits you best.
If you consider that (1) each of the recommended textbooks is about 400 pages long, (2) the NPPE exam blueprint/syllabus diverges completely from the organization of the textbooks, (3) there are many topics in the blueprint/syllabus that you cannot find in the recommended books and vice versa, (4) that beyond reading these books you will still need to do some further research for those missing topics, then, as the NPPE Candidate Guide advises you to take the path that suits you best, you are probably better off reading a single book that contains all the topics of the exam. A great candidate is of course the book “Engineering & Geoscience NPPE: Law and Ethics” by WPE Studio as it is only 240 pages long, covers all topics of the exam, and is written following exactly the organization of the NPPE blueprint or syllabus. This can truly streamline your NPPE prep and be very helpful to monitor your progress.