First let me congrats you for the book, I bet it was an amazing experience.
Now the question
Do I need to be a machine-learning professional in order to use Apache Mahout?
For example, Apache Hadoop made it possible to write massively clustered and distributed Map/Reduce jobs without being parallel computing expert.
I don't think you need a machine learning background to understand and use the project -- but you might need a guide, like the book! It is, at the moment, a collection of interesting code, and a workshop for some valuable ideas, but is not well documented or explained. The book tries to help bridge that gap. (And the book only assumes you have some Java experience and standard math background, not deep machine learning experience.)
Some machine learning experience would probably help understand the ideas quicker, but what you really need to use the code is a willingness to read the source and experiment!