The overall direction is not wrong: The Concept of Irony truly is the central and foundational work for Kierkegaard. But the author doesn't really have that sensitivity regarding Kierkegaard's use of pseudonyms, and more importantly the author's whole writing defeats the purpose of Kierkegaard's irony.

However, plainly, this is an introductory work, written for audiences without even a knowledge of Socrates, Hegel, Fichte... hence many depth cannot be revealed (granted that they can in principle be explicated), especially when the reader hasn't faced the difficulties that Kierkegaard was confronting himself.

Kierkegaard is an immensely difficult and profound thinker. He's not technically, verbally, difficult, but philosophically difficult. He has no set positions, it is in the dialectical process, in the very process of feeling, thinking, etc. that the essence of his thought lies, not in various conclusions and positions. It's ill-advised to write an introductory exposition to his thoughts, unless the author himself is a profound thinker and a literary master. The author of this book certainly is not the case.