The manner of input is a legitimate form of interactivity. I grant that input-interaction may be almost completely separate from content-interactivity, and I acknowledge that CYOAs are inherently better at providing content-interactivity.
Being able to interact with the narrative (which is different from the story content) is important to immersion. The other part of immersion is detailed simulation/world-modeling. A CYOA may be able to equal or exceed any IF game for interactivity, but I feel that parser-IF is unequaled when it comes to immersion/mimesis (except perhaps for MUDs, which share both the parser and the simulation).
When I read The Wheel of Time, no matter how much I am immersed in the story and how fascinated I may be with the world-building and mythopoeia, I can never live the story of those static books. I may deeply identify with the character of Rand al’Thor, but I can never see through his eyes. In order to do so, I would need to be able to construct the vision in my imagination and manipulate it, but I can’t do that with the book, because it will not interact with me. If The Wheel of Time were a CYOA, I might be able to interact with the story and characters for almost endless possibilities, and that would be great fun. However, I still wouldn’t be much closer to being able to construct the world and live in it.
However, the parser interface of Fallacy of Dawn allows me to see through the eyes of Delarion Yar and live his story, which (along with Robb Sherwin’s great writing, of course) makes him so real and sympathetic.
Parser-IF that isn’t interactive on a story level still has to offer something that static novels lack. It’s going way too far to compare the use of the parser without story interaction with cutting up a novel and rearranging its pages. The first IF game I ever played was Wearing the Claw by Paul O’Brien, and there’s no way to get different endings (other than, I think, a simple loss that can be undone) or to affect any variables in the plot. In fact, Wearing the Claw is linear as a puzzle game; you can’t do things out of order because you are only presented with one problem at a time. And yet, I was totally captivated by that game, and because of that I am still playing IF today, about nine years later. The game let me live the story in a way that no static fiction I had ever read could ever have, and it did this with a parser and a simulation without need of story-interactivity.