He ends up drawing a Venn-style diagram which has an outer circle labeled with "critical thinking" and "rational analysis," within which is a series of three overlapping circles labeled "atheism," "skeptical inquiry," and "political philosophy." He argues that skeptical inquiry only overlaps with atheism where religions make empirical claims that are subject to scientific investigation, and likewise for political philosophy.
I offered a few critical comments at his blog, noting that it is odd that "atheism" is the only label on his diagram which is the name of a specific position rather than a method or discipline, and suggesting that it be labeled something like "views on religion." I also suggested that that circle extend beyond the scope of the "critical thinking" and "rational analysis" circle, though that's presupposing his diagram is descriptive rather than normative. [Note added 1:31 p.m.: If his diagram is understood as a diagram of what is appropriate subject matter for critical thinking, rational analysis, and skeptical inquiry with respect to atheism and political philosophy, then those two circles should arguably not extend outside the border of critical thinking/rational analysis.] Similar considerations should apply to the "political philosophy" circle. People hold religious and political views for reasons other than those produced as a result of critical thinking and rational analysis.
I also took issue with his identifying "skeptical inquiry" with scientific skepticism. Skeptics have always used philosophical tools as well as scientific ones, but I would find his diagram more accurate if the middle circle was labeled "scientific skepticism" or even "scientific inquiry."
I also have some skepticism about this taxonomic enterprise in general, which is arguably both philosophical and political itself--Pigliucci is not using scientific methods to set up this framework, it's philosophy, and there are political and pragmatic reasons for wanting us to accept it--to issue in a ruling that certain domains are off-limits for skepticism, namely the examination of religious and political claims that are not subject to empirical investigation.
I think there are good pragmatic reasons for skeptical organizations to restrict themselves in such a way--the methods of skepticism can be used by anyone, regardless of their political or religious views, and organized skepticism has tried to appeal to a broad audience to focus critical attention on paranormal claims where scientific methodology can be brought to bear. But I'm skeptical of this as a general picture of the applicable domain of the methods of skepticism or skeptical inquiry. (I should note that I don't think that atheism implies skepticism--thus the reason for extending a circle with that name outside the boundaries of critical thinking and rational analysis--nor that skepticism implies atheism. Skepticism is about the methods used, not the conclusions reached. An atheist might think that any consistent application of skepticism will lead to atheism, but that presumes both that atheism is true and that consistent application of skepticism is a guarantee of truth, which it is not.)
I agree with commenter Maarten that the boundaries of these circles are fuzzy--just as the boundary between science and non-science doesn't admit to a bright-line demarcation. People can conceptualize the boundaries differently, even granting Pigliucci's conception of "empirically investigatable" as the domain of skeptical inquiry or scientific skepticism. The boundaries between scientific disciplines are themselves fuzzy and they use different methodologies, with huge differences between experimental and historical sciences, for example.
Finally, I agree with commenter Scott (Scott Hurst), who observes that religious believers do make very specific claims "about the nature of the universe, how it works, and its history (including our own)," and specifically noting belief in the power of prayer. These things are empirically testable and do make at least some common (one could say "vulgar") conceptions of God and religion refutable by science. The fact that a more sophisticated believer or theologian can construct a view that uses the same words yet withdraws from the realm of the empirical doesn't mean that the vulgar conception hasn't been refuted. This is perhaps more obvious with modern religions such as Mormonism and Scientology, where in the former case historical evidence and DNA evidence falsifies some key claims, and in the latter case where scientific evidence falsifies a great number of its claims. Hubbard's cosmology, for example, includes the idea that Xenu dropped thetans into a volcano on Hawaii 75 million years ago, but Hawaii didn't exist 75 million years ago. His book History of Man includes Piltdown Man in the human lineage, even though that fossil was discovered to be a hoax shortly after the book was published. And so forth.
It's fine for Pigliucci to define and use the terms the way he wants, but I don't think he's given strong reasons for the rest of us to accept the specifics of his formulation.
UPDATE (October 24, 2009): Russell Blackford has written "Pigliucci on science and the scope of skeptical inquiry" at the Sentient Developments blog, which comes to similar conclusions with a somewhat more comprehensive argument.