Who is the instigator of the action in this combination?

I interpret it as I don’t like the fact he’s reading books. I don’t completely understand either of your interpretations.

So, you interpret it as the instigator is HE. Can “his book” be the instigator?

I can’t read any way “his book” could be the instigator.

Your second interpretation would only make sense in a very specific situation (where someone has some kind of living and literate book). That would be a very unusual case that requires a particular context to force someone to reinterpret the normal meaning of the words.

Absent all of those special circumstances, the second interpretation cannot come up. So if this were a test question, for example, the second interpretation would not be a legitimate answer. It’s an incorrect interpretation that can only be forced to be correct by manipulating the surrounding information.

If you wanted to say the second, you would have to word it as; “I don’t like the book he is reading.”

It could be one of those two interpretations. It could be, as @Hawaii_Jake said, “book reading” is an act…reading books all the time. It could be that you are listening to an audiobook and you don’t like the way the book is being read, in which case you are now looking at the reader as the instigator.

To me, “I don’t like the way his book reads” suggests that he wrote the book. It’s “his book” because he’s the author, and his writing style is somehow awkward, difficult, or otherwise unpleasant to read.

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I like the following sentence.
“I didn’t say she stole the money!”
Depending on how you say that, and which word you emphasize, it will mean different things.