An academic paper in computer science usually consists of applying a well defined "technique" to a well defined "problem." For example applying "Support Vector Machines" to "Text Classification" or applying "Expert Systems" to "Medical Diagnosis" or applying "Particle Filters" to "Robot localization"
The crux of what Newport is referring to is that in practice, many(most?) academic researchers don't deeply learn new techniques that are outside of their immediate research agenda after leaving grad school. They will certainly be AWARE of new techniques and might learn their high level ideas but they won't really learn them deeply enough to be able to improve them or use them in a non-trivial way. It is much much easier to continue exploiting and building upon the techniques they have already mastered than to invest several painful months(years?) to master completely new techniques.
So what Newport is suggesting that you should stop applying your current methods that are easy and very productive for you and make a substantial investment of time and energy to master the latest techniques - even if you don't exactly know how you're going to apply them
A programming analogy: If you're a C++ programmer, stop doing C++ projects and spend at least 3 months until you're an expert in Python. If you're a Python programmer, stop writing Python and invest several months in becoming an expert in Go. (the analogy is not perfect because mastering a new language is probably a bit easier and more fun than the kind of things Newport is talking about)
Here are a couple of thoughts I had on this:
(1) How applicable is this idea outside of academic research? For example, in academia there is a big reward for being the FIRST person to apply a given technique to a certain problem, but outside of research being the 2nd or 3rd person to do something can be just fine. (See: Friendster, MySpace, Facebook). So maybe you can afford to wait until someone has shown a great application of a new technique and only then jump in and try to exploit it.
(2) An opposing but also convincing idea is that it is better to focus your efforts in one area to avoid spreading yourself too thin. Such focus allows you to gain "comparative advantage" and to easily do things that are difficult for people who don't have your deep experience. In other words, it is better to spend your efforts trying to become the world's greatest Python hacker than to jump on the bandwagon of every new programming language that comes out and ending up as a "Jack of all trades, master of none."
My conclusion: I do think it is worthwhile to challenge yourself not to just stick to what you already know (which in my personal experience is VERY easy to do especially if you find that you're very productive using what you know). But you also have to be selective. Life is too short to try to be a master of everything. And there is great value in gaining a very deep expertise in a particular topic or technique.