Ink is more suited for embedding in a game which adds additional presentation or gameplay stuff on top of the text, using some other language/engine (like Unity). It will handle the text stuff, and provide hooks/bindings for the rest of the game to use.
Whereas, in Ink, IIRC the flow is like scrolling text. New passages appear below the older ones, depending on choices made. I don't know a lot about Ink to be honest.