No, the Game Book is not a required supplement with Foundations or Essentials. Each Foundations Teacher's Manual and Essentials Teacher's Guide includes instructions for many games played in the lessons. Many of students' favorite games are included in both the Game Book and the curriculum.
That said, the Game Book can still be a helpful addition! Games are a wonderful way for students to build fluency and automaticity with the skills they are learning and are often one of their favorite parts of Logic of English curriculum. You may find the Game Book helpful as a resource for even more practice ideas to add to your Foundations or Essentials lessons! There are additional games that are not included in the curriculum. Additionally, there are new master templates, as well as helpful lists of sample words for practicing various skills (high-frequency words, -ing words, compound words, silent E words for each silent E rule, long vowel words).
The Game Book is also an excellent resource for any language arts curriculum, Sounding Out the Sight Words, and Orton-Gillingham programs.