In this book, Bogost analyzes the history of rhetoric and argues that videogames are part of a new form of rhetoric since their procedurality involves interaction. He calls this new form of persuasion Procedural Rhetoric, and develops his argument by comparing videogames to the characteristics of computers and by analyzing the influence that videogames can have on politics, advertising and education.
Bogost develops this argument by first analyzing the notion of "procedurality," then the idea of "rhetoric" and then combining the two to form Procedural Rhetoric.
After briefly discussing the negative connotations procedure often has, Bogost cites Janet Murray who gives a technical definition for procedure within the context of digital artifacts as the "defining ability to execute a series of rule." Bogost restates the this definition as the fundamental activity of software authorship and discusses how the procedure of computers is what "fundamentally separates them from other media."
On a more philosophical level, Bogost discusses how all behavior is underpinned by logic and implies that the procedurality of computers (and thus videogames) is in fact not unique to digital media. Nevertheless, it is obvious that the interactive procedurality of videogames and computer programs is unique these digital media when they are analyzed as cultural artifacts. Overall, Bogost views the procedure of videogames as devices for expressing ideas and forming arguments, he compares them to "metaphors" and other literary devices.
Bogost begins his exploration of the term rhetoric in a similar way he begins his explanation of procedure: in both cases, Bogost makes an effort to dispel the negative connotations these terms have. Through a discussion of oratory rhetoric, visual rhetoric, digital rhetoric and procedural rhetoric, Bogost arrives at a definition of rhetoric as "effective expression."
According to Bogost, oratory rhetoric is privileged in the eyes of many, while written, visual, and digital rhetoric are under-appreciated. Bogost concludes his section on rhetoric by suggesting that digital media must focus on procedurality in its study of rhetoric. 
Combining the two: Procedural Rhetoric
Bogost combines these two terms to define Procedural Rhetoric as "the practice of using processes persuasively." He states that he will use videogames as an merely as an example of Procedural Rhetoric. So in a certain sense, the arguments made in Persuasive games have larger implications about the nature of all digital media that has a Procedural Rhetorc--all interactive digital media rhetorically make arguments through their interactivity.