It's refreshing to learn that you knew much of this; but you'd be surprised at how many people don't!
Defining spirituality is always tricky, as it means different things to different people. But in the context of this article, it refers to people who evidently practiced, followed (and often made contributions to) a religious tradition premised on a reality that transcends the material world. Mystics are those who pursue (sometimes claim) some form of direct connection to that reality. The reason that this worldview often corresponds with polymathy is that it tends to be holistic by its very nature - encouraging the study (or at least acknowledgement) of various dimensions of the world as well as their interconnections.
Specialisation - if we are to define it as the pursuit of mastery in a particular skill or field of knowledge - is certainly commendable. In fact many people do achieve this in many fields. That said, even the notion of the ‘specialist’ requires revision. Yes, a specialist ought to have a deep knowledge of his or her subject area, but that depth should be given perspective by breadth too. For example whilst specialist training is of course important for medical practice, to become the best doctor or healthcare practitioner you can be, you will have a rounded understanding not only of the complex, multifaceted biochemical and physiological system that is the human body, but also the social scientific, humanistic and cultural contexts within which it operates. So a true specialist is actually a polymath.
But specialisation as an institutionalised system and cultural norm is nothing short of intellectual and professional apartheid - it has a long history of exploitation. Whether in the form of industrial division of labour or the caste system, such social engineering confines people to silos and bubbles, often for life. Not only does this foster ignorance, bias and narrow-mindedness, but perhaps more importantly it thwarts one's ability to fulfil their many-sided potential.
Wishing you every success in the multiple facets of your life.