You did call it a game in this thread and not a book. So to you it is a game. And to my understanding it is not a book if it is meant to be interactive.
While the level of interactiveness is debateable for a chose your own adventure book or something like a kinetic visual novel where you only press next, those do require software to run. I cannot print your "gamebook" and read it on paper. You would have to create a printable format where I could then turn the printed pages manually instead of using a software to navigate per hyperlinks. Then your gamebook would be a book, instead of a twine game.
But opinions vary. Other devs also think, their twine games are books. https://itch.io/books/tag-twine
I suggest you look at those to see examples for screenshots and gamebook descriptions.