The author has fallen into nihilism and has mistaken it for Buddhism and mindfulness meditation. Buddhism warns against falling into nihilism like this, but I suspect mindfulness meditation practices do not.
Anatta doesn't mean no-self. It's a complex concept and is often mistaken.
Anatta has two parts to it:
1) Reality is broken up and labeled as two kinds. There is the present moment reality, before it has been labeled by the mind called paramārtha, and a reality of abstractions and labels over the first reality called saṁvṛti. (For further reading checkout the Two Truths Doctrine.)
Self is an idea, so it exists within saṁvṛti. Self is an abstraction, as is everything in this reality.
2) The abstraction of self is a combination of a bunch of elements, eg body, mind, and so on, to make the concept of self.
Anatta, then, is a set (Set Theory). In the ultimate reality of paramārtha there is no self. In the thought form reality, self is an aggregate/abstraction.
"Why teach this?" you might be thinking. Because it doesn't seem like that big of a deal. It's even obvious on a second examination.
The reason this is taught is if one thinks a thing is them (like their work) and that thing gets insulted, they instinctively feel like they need to defend it, which causes a lot of dukkha (psychological stress). If one realizes that thing is not them, then there will be no dukkha when it is criticized.
People mix up anatta (non-self / no-singular-self / no-soul) with no-self. No-self is a meditation practice, similar to noting, which one realizes bit by bit, every single thing that comes into their mind is not self itself, even if it is a piece that makes up the abstraction. All abstractions are made up from a series of parts.
imho, anatta doesn't need to be taught to do mindfulness meditation, but understanding impermanence is important, because without it most people try to fight stressful thoughts and change them, instead of thinking of them like rain clouds, to be observed, not modified.
Once the meditator sees the causal chain from observation to thought, action, or feeling, that is all they need to change their habits and live a happier and healthier life.