The distinction between literary genres does play an essential role in New Criticism.

The correct answer is William Walwyn.

To understand the context of this question and the correct choice, we can analyze the two primary components presented: the theoretical statement regarding New Criticism and the historical figures listed in the options.

1. Analysis of the Statement on New Criticism
The statement reads: "The distinction between literary genres does play an essential role in New Criticism."
In literary theory, New Criticism is a formalist approach that emphasizes close reading of the text as an autonomous, self-contained aesthetic object. New Critics prioritize the internal structure, tensions, ironies, and paradoxes of a text over external classifications such as authorial biography, historical context, or rigid genre categories. Consequently, they often apply similar close-reading methods to prose, drama, and poetry alike, frequently referring to any literary work under analysis broadly as a "poem." Thus, from a theoretical standpoint, genre distinctions do not play an essential role in the New Critical framework.

2. Context of the Options
The options present a mix of 17th-century political tract writers and modern literary critics:
• William Walwyn: An English merchant, pamphleteer, and key leader of the Levellers—a political movement advocating for popular sovereignty and religious toleration during the English Civil War. He is the author of several influential pamphlets, including The Power of Love (1643).
• Gerrard Winstanley: An English reformer and leader of the Diggers (True Levellers) who advocated for communal land ownership.
• F. R. Leavis: A highly influential 20th-century British academic and literary critic.
• George Saintsbury: A prolific late 19th- and early 20th-century English literary historian and critic.
Based strictly on the provided answer key, William Walwyn is identified as the correct option associated with this item.