Key points of Wagner's theory of innovation
Wagner does not propose any new theory. He uses the word innovation to mean evolutionary adaptations that manifest qualitatively different traits. In fact, he has himself not defined it properly in the mentioned book. This is what he has written about the term innovation:


  It may be difficult to define rigorously what an evolutionary
  innovation is [538,616]. However, these and countless other examples
  show that it is usually easy to recognize: a new feature that endows
  its bearer with qualitatively new, often game changing abilities.
  These may not only mean the difference between life and death in a
  given environment (just think of biosynthetic abilities), they may
  also create broad platforms for future innovations, as did innovations
  of photosynthesis and of complex nervous systems.


However the examples he cites in the introduction are not as obvious as he says. Lets say the evolution of nervous system. The innovation that would have led to evolution of nervous system could have been the evolution of electrically excitable cells.

Actually, throughout the introduction he does not actually clarify the meaning of innovation. In page-3 he does list some features of innovation but it is all still vague. Without a rigorous definition nothing is easy to recognize and classify (especially in theoretical terms). 

I do not have the book and cannot look through the entirety of it. However, based on what I have read in some of his papers I can comment something about what he possibly means by innovation.

In certain dynamical systems, some parameter changes can lead to qualitative differences in the output (bifurcations). Steven Strogatz's book on Non-linear Dynamics and Chaos is a nice and easy read on this topic.

If you look at some of Wagner's research papers, you would understand this idea better. Some of these papers are about how some parameter changes can affect the overall outcome (which may be drastic). For example, in this paper the authors talk about how differences in cell division rates can affect the outcome of a cell differentiation event. 

He also talks about metabolic innovations which refer to changes in metabolic reactions and network leading to new products/optimized growth etc. Details of this can be found in his lab's papers on Metabolic Flux Balance Analysis. 

There is nothing new or drastically different about all of this. This is just an addition that was unknown during Darwin's time. All that he says is still quite in agreement with the current evolutionary theory. (But personally, I find the opening of the book too vague).

As far as empirical corroboration is concerned, you may have a look at his lab's research papers.