This is common in scheme -- to build sublanguages embedded in scheme.
Friedman builds a sublanguage for his own needs (in the last chapter it builds a full interpreter for his language).
For his purposes he builds his own data structures and each structure has its own axioms. Do not confuse scheme's structures with the structures embedded in scheme he builds. He uses scheme's operators to build his structures, but the axioms of the language he builds are not the same as the axioms of scheme -- scheme is larger. In other lisps or embedded lisps you will find other axioms for the same structures. To make a comparison, the compiler GCC compiles C, it recognizes C as input and it is itself written in C, but the embedded languages it implements at different stages are more complex than C itself (C can be seen embedded in GCC and GCC extends it with many structures (apart from the intermediate languages that are not C) in order to facilitate the writing of the compiler itself).
To understand this better I recommend you to read Anatomy of Lisp
-- it is older than SICP, but it's excellent nowadays to understand the foundations.