the author left God out on purpose. It is not a mystery. Just read a bit about the meaning of the story and the literary style. It is pretty evident that it is a literary technique.
The RCC version of Esther has been shown to be invalid, as we all now know that God was added into the book hundreds of years later. Not to mention that doing so totally destroys the author literary genius and artistry. If the RCC truly believes that the book was inspired by God, why did they feel it was necessary to fix it? By fixing it they have broken what makes the book an amazing work of literary art.
People like Martin Luther misunderstood that not mentioning God or any of the Jewish spiritual rituals (except fasting) was used by the author to focus on the meaning of the story. That is why Luther said it should not be in the canon. By the way, as I understand it Luther did not say it was not an inspired book, but just that it should not be included in the canon because it did not mention God but also because it does not point to Jesus and the cross. Maybe elsewhere, where I am not familiar with his writings, he did mention it was not inspired. But from what I have read he is just saying it should not be there because it doesn't mention God and doesn't point to Jesus. He said the same thing for Ecclesiastes, Song of Solomon, James, and Revelation. His definition of canon was a bit different than how we'd define it today.
The meaning of Esther is multi-fold as a historical document of the origin of the Feast of Purim and the life of Esther. Most scholars believe that it was written for Jews that did not or could not return to Jerusalem during the rebuilding (about 30 to 50 years before Ezra and Nehemiah). But the message of the story is along the lines of God's providence for the people of God.... even if you do not see God working in your lives or acknowledge him, he is there and working.
Literary critics find the literary artistry in Esther pretty amazing and more so when you consider the book is some 2500 years old +/- a few years. Other contemporary literature were basically contracts, government decrees, laws, and a couple of not so well written cuneiform stories that in no way compares to the depth and skill of the author of Esther. Just consider that even today people are drawn to the story and message of Esther. That says a lot of the author and the technique used in the story. I for one find that absence of God in the story on one hand, and then at the same time the providence of God on every page, to be an amazingly beautiful literary technique. It worked to capture my attention and bring the message home to my own reality and life.