I suspect the author is exaggerating a bit when he says it's the only way he thinks. I also have the "narrative voice" but I absolutely can think about things without the voice, it just doesn't feel as much like "thinking", if that makes sense.
There are some things that are explicitly visualized, like an object I'm thinking about, where I wouldn't say in my head "I am imagining the sun. It is bright. Etc. etc.". I'd just picture the sun, and my "narrative" would probably be about why I was thinking about the sun, not describing it.
Same applies for more abstract concepts, just without the visualization.
This is how it seems for me, too. When I pay attention to what I am doing, it seems as if I am thinking in complete sentences, but if I then try to write down the idea that I have just been thinking about, I find that it takes a lot of editing to turn it into coherent language. Furthermore, I cannot really say anything about what it is like to think when I am not paying attention to doing so, so maybe it is just how I explain my experience of thinking to myself.
Perhaps experiments using techniques such as PET scans might reveal if there is something more characteristically linguistic going on in those of us who feel we have an internal monologue.
There are some things that are explicitly visualized, like an object I'm thinking about, where I wouldn't say in my head "I am imagining the sun. It is bright. Etc. etc.". I'd just picture the sun, and my "narrative" would probably be about why I was thinking about the sun, not describing it.
Same applies for more abstract concepts, just without the visualization.