Google Ngram is an interesting way to track the usage of various words and terms.
Here you can see the steady rise in the use of the term "entrepreneurial economy."
And here you can see how the use of "information economy" has begun to fall (even though it is still used considerably more than the term "entrepreneurial economy").
So apparently a long way to go but the fourth economy does indeed seem to be (oh so slowly) gaining on the third, information economy in terms of mention in writing. My argument is that it is emerging but we're still not quite attuned to it so it is becoming harder to ignore but still not completely appreciated.
Oh, and for bonus points, here are the three most recent intellectual revolutions. Given we build on each previous stage, and given that we've had centuries to become aware of the importance of the Enlightenment and Pragmatism, it makes sense that systems thinking is only now beginning to rise in general use and awareness relative to those.