In some contexts, especially logic programming, the word interpreter describes what this book calls an engine. In this same context the word interpreter may also refer to the combination of the engine and the parser that accepts a programmer's commands. This book uses engine rather than interpreter to refer specifically to the object that can sift through data looking for matches to a query.
Another reason this book avoids the word interpreter is that the interpreter pattern, as [Gamma et al.] document it, associates interpreters with languages. The engine that this book develops is language-independent, and it does not follow the interpreter pattern.
For these reasons, this book describes the object that powers logic and query languages as an engine.