My experience, as a native English speaker who has learned German as an adult, is that different stages in language learning benefit from different kinds of study. There have been times where memorizing grammar rules have been enormously helpful to me, others where reading a lot is what I needed, and still others where holes in my vocabulary were holding me back. After a certain level of proficiency, the only new thing you encounter in the language is unknown words and phrases, so it makes sense to focus on learning them.
> Words in one language do not have a one-to-one mapping with words in any other language.
As you have mainly studied non-European languages, this might be more true in your experience than for those who are focusing on European languages. There are certainly many words that map one-to-one between German and English, especially in common usage.
What I like about the author's technique is that it seems like a smart way of priming the pump for real and detailed learning: when he encounters a new word in the text, he has a general idea of what it means from the definition, but he can sharpen that meaning with the particulars of the context where he finds it. Otherwise, he might get only the vaguest sense of what a word means from context, or have no clue at all.