Though, they have an interesting definition of "unitarian." Theological line drawing -- especially the vexing question of "what is Christianity" -- by its nature invites disagreement. This book includes not just Arianism and Socinianism as unitarian doctrines but also Sabellianism. That doctrine teaches a divine Trinity -- Fathers, Son, and Spirit -- existing in ONE person, not THREE. Swedenborgs and "oneness Pentacostals" believe in, if not Sabellianism, something similar to it.
As the book notes:
The word Unitarian, in its most general signification, denotes one who believes that God exists in one person only, in contradistinction to one who receives the doctrine of the Trinity. Under this generic name, however, are ranged several classes whose views differ widely from each other. Of these, the most prominent are the Sabellians, who maintain that the Word and Holy Spirit are only different manifestations or functions of the Deity; the Arians, who believe that Jesus Christ is neither God nor Man, but a Superangelical Being; and the Humanitarians, who regard Him as a mere Man. In respect to the influence of Christ's death, some suppose that it contributes to our pardon, as it was a principal means of confirming the Christian religion, and giving it a power over the mind ; in other words, that it procures forgiveness by leading to that repentance and virtue which constitute the condition on which forgiveness is bestowed; while others maintain that this event has a special, though undefined, influence in removing punishment, as a condition of pardon, without which repentance would be unavailing. Unitarians are generally Arminians, and most of them believe in the ultimate restoration of all men to holiness and happiness in the next world. But, in regard to the measure of authority that attaches to different portions of Scripture, as well as in respect to many of the details of Christian doctrine, there is great diversity. All, however, unite in rejecting human creeds as of no binding authority. Some idea may be formed of the very diverse views which are included under the general term,— Unilarianism, by comparing the sketch of Dr. Bezaleel Howard, or of Dr. Hezekiah Packard, with that of Dr. Priestley.
I'm not sure if it's proper to categorize Sabellianism as "unitarianism." It certainly isn't "orthodox" though. Previously when confronted with Sabellianism or like doctrines I recognize such as "heresy," but categorize them as neither unitarian nor trinitarian.
Though in categorizing Sabellianism as "unitarianism" that enables the book to capture even more notable Founding era preachers as "unitarians."
If those who don't believe in the Trinity, even Sabellians, are not "Christians" a heck of a lot of notable Founding era preachers were not "Christians."
Whether the historical-theological proposition is true is debatable. But it makes for a very interesting dynamic. The "Christian" or "Deist" question is such a false dichotomy. Here is a five point breakdown from most to least "orthodox."
1) Orthodox Trinitarians; 2) Sabellians; 3) Arians; 4) Socinians; 5) Strict Deists.