Shakespearean discovery of the modern mind
Solution 1:
It is essentially a reference to Harold Bloom's influential book Shakespeare and the Invention of the Human.
Bloom's wildly audacious book posits that Shakespeare invented the modern milieu of existence.
The only book I know as audacious as this — and somewhat similar — is Julian Jayne's The Origin of consciousness in the breakdown of the bicameral mind, which posits that Homer (The Odyssey, The Iliad) merely essentially invented human consciousness as we know it.
Furthermore, the presenter you mention, David Simon, simply goes on to explain in the quote you gave what Simon means, his take on the "Bloomian idea" if you will: to wit, Simon feels that only with Shakespeare did we move from "indifferent Gods control us" mode to today's "we control everything" consciousness.
As a language-consciousness freak, I love reading about ideas like this. A third point here is the novel Snow Crash by bizarre sci-fi/consciousness/whatever writer Neal Stephenson, which deals with the "memetics", if you will, of the early days of consciousness in humans (say, 50,000 years ago).
In short, when Simon says "the Shakespearean discovery of the modern mind," it's a riff on Bloom's Shakespeare and the Invention of the Human.
Solution 2:
This just points up the contrast with the modern view that "anything is possible as long as we will it" vs. the fatalistic Greek notion that we are playthings of fate (i.e. "the gods") who may do things to hasten our fall but nothing to prevent it.
I feel obliged to point out that, as much as I admire The Wire, that excellent series of David Simon's, I'm not sure I would agree that his analogy about Greek drama is accurate to several decimal places, nor is his contention that Shakespeare discovered "the modern mind" in his plays. In fact, in Form and Meaning in Drama, H. D. F. Kitto, a noted expert in classical Greek literature and theater, devotes a whole section of this book about Greek drama to an interpretation of Hamlet as an exemplar of Greek tragedy. I can't think of a single one of Shakespeare's tragedies, in fact, which I would think of as being about self-actualization. Think of his "star-crossed lovers" in Romeo and Juliet or the ambition of Macbeth that actualizes only his own demise. (Really, David Simon, I love your work — but shut up about things you haven't thought through!)