Translate 主播 in this context
You are correct. 主播 (anchor person/ program host) makes no sense in this context

The one who read out the content in an 有聲書 (Audiobook) should be called  "誦讀者" (one who recite text) 

Or "朗讀者" (one who recite text in a clear voice) if the content is of poetic nature 

阅读者 mainly mean the one who read (with eyes, not reading out with voice)

I own a few Audiobooks, the one who read the book out is listed as "narrator" (叙述者), So. 叙述者 could be used in Chinese Audiobooks titles too