There is no 'need' to get both the app and the e-book, but you may want both, in which case we can hardly blame you! :)
Here are some things to keep in mind while you decide:
Subscribing to the app is awesome and provides you access to ALL of the Jessie's Girls Training Programs (except Prenatal) as well as her daily workouts and a pretty sweet macro calculator. The app also walks you through each workout with a video for every exercise, as well as additional videos explaining several terms you will encounter within the program.
Purchasing an e-book means you get to keep your program FOREVER! It also allows you to look through the entire program at once, as opposed to only being able to see your current day's workout in the app. In the e-book you will find all of the information needed to calculate your macros for your body, and how to adjust those macros based on your goals.