Unlike the author, I do dream visually (in fact, I tend to have very vivid dreams; the most vivid ones are difficult to separate from reality, even if the subject matter is something fantastic like being part of an interstellar military or something). If I'm in a state between waking and sleeping I actually do have much more of a mind's eye, but when I'm fully awake I don't have pictures in my head...but I remember what it's like to visualize things mentally because of my dreams.
I have at least something of a "mind's ear" in that I can hear music in my head (the detail is usually not as rich; it's often just the melody with lyrics). Additionally, I have a very good memory for song lyrics and when I listen to music the concept of tuning out or not being extremely aware of the lyrics is something that friends I have described but that I rarely experience. I can usually only tune out lyrics in music if it's a song that I'm already very familiar with.
One aspect that I find interesting is that although I can't really picture places I still have spatial awareness in my mental concept of them. For example, if I remember one of the houses we lived in as a child I can "place" various objects in and around the house in their correct spatial relationships without picturing the objects themselves. Do other people with aphantasia also have this experience?