Author here. Yes. Texts says "If classical logic is based on set theory", that is I am comparing the relations to set theory and category theory to that between classical logic and intuitionistic logic. I will try to fix the ambiguity.
"If we view classical logic as based on set theory, then intuitionistic logic would be based on category theory and its related theories."
And regarding the fact that CT is not "needed" for algebraic logic what I say is "category theory and its related theories." where I consider orders related to categories.