Avoiding the Susan Greenfield issue, the topic is definitely worthy to ponder for a moment. I'll speak about myself, and in doing so, suspect that I speak for many of us.
Already, my machine is performing a very important role for me: it's my memory. My e-mail archive is a living memory of all the conversations I've had, which means something rather profound: that I don't have to remember the literal data that were provided, e.g., the specific wording of a decision, but instead, that such a conversation happened at one point, and was tracked via e-mail.
Beyond this capacity, let's address the point of TFA.
It's well known that neural circuity develops as a human spends more time with something, e.g., a talented musician has larger areas of cortex devoted to the things that make a talented musician talented, e.g., hand movements, musicality, etc. Whether these areas are separate, e.g., modular, and/or if they're represented as an integrated system is a conversation for another day. Suffice to say that brain areas expand as a human practices things more.
So it's fair to say that using technological tools in the commonplace way that we do builds neural matter that support our expanding use of the same. Whether this is at the expense of other skills, neurally, we don't know.
On the other hand, how many of us take the time to bake our own bread, fix our own cars, and plow our fields? It's fair to say that we spend less time building the products for our basic needs, which means that we develop those skills - and the related neural matter - less
So, while the author of TFA may (or may not be) a lady with a funky background, clearly the idea has merit and its implications - tradeoff of neural representation in areas of skill - is important to consider as we expand our use of social and media devices, and decrease the time we spend developing our ability to perform other tasks (supplanted by technology, as it were).