We often use the present progressive (progressive aspect is another name for the continuous aspect) not to refer to something that we are literally doing right now, but to something that we are broadly doing on an ongoing basis.
The perfect continuous, "I have been working on my new book", would indicate that they weren't doing it right at that moment, but also wouldn't give any indicate that they would work on it again. "I will be working on my my new book" indicates that they will work on it in future, but not that they are working on it now, nor that they have already worked on it at all. Using the present progressive indicates, depending on context, that they have been doing so, and that they will be doing so, and that they might be doing it wright now.
You can't use it for every verb in every context. "I am running" would usually suggest that you really are running right now. However, if the question was "what are you doing for exercise?" - also a case where the present progressive is used but doesn't mean literally right now - you might answer "I am running" even though you're currently sat in a chair in your doctor's office. Or you might say "I'm running a lot" without it being an answer to a question, just as a general statement, and the addition of 'a lot' indicates that you are speaking in general, not about right now.
The examples that come most easily to mind are all to do with pieces of work that don't get finished in one sitting. "I'm carving a replica of Michelangelo's David", "we are developing new policies", and so on. However, I can't think of any verb that would never be used in the present progressive to refer to an ongoing process that isn't literally going on at the time of the statement.