Our dictionary defines the word "manifesto" as "a public declaration of motives and intentions, as by a political party or by an avant-garde movement." The statement reportedly made by the suspect in New Zealand did not come from a political party and it seems euphemistic to refer to him as being part of an avant-garde movement. The word "manifesto" also may elevate such a statement, in the eyes of those who might want to copy this person's actions, to something more than it might really have been.
It has some aspects of a "manifesto," but can certainly be described as a "statement." Another option: "screed" (defined as a "long, tiresome speech or piece of writing").