Definition by Jisho.org - the place for; the time for; the level of (usu. with neg. sentence; indicates that what precedes it is at odds with the seriousness or true extent of the situation)
So basically どころではない（じゃない, etc) means
This is not the place to be doing xx, and it comes with a bit of a
self-restraint(我慢) because of the environment or social status of the place, or the people around you (IMO).
So let's first analyze the two "wrong" sentences.
B) 字が小さくて、この本を読むどころではなかった。- The book was small, so it wasn't the right thing to read it.
This does not make sense to me, as the reason to why it was a bad idea to read the book.
C) 眼鏡がなくて、この本を読むどころではなかった。 - I did not have my glasses, so reading this book was not the right thing to do. (it was no place to read).
This sounds more like being "incapable" of reading, rather than the
self-restraint nuance that this construction carries, so it doesn't fit. Something 「眼鏡がなかったので、本が読めなかった」would've made sense instead.
Now the correct answer:
A)来客があって、この本を読むどころではなかった。I had a visitor, so it wasn't the right place for me to read this book.
Here, the social norm dictates that it would be impolite to be reading the book because you would be ignoring the visitor. Which makes the person
self-restraint and not read the book.