The deeper point here is that the idea of the moderate middle is bullshit: it's a rhetorical device meant to marginalize some policy positions at the expense of others. There's no actual way to measure it, or consistent definition animating it, and it doesn't spontaneously emerge in any of the data.As someone who would likely be mischaracterized in a survey as a moderate, I completely agree. The way pundits, journalists and pollsters measure and discuss moderates is indeed meaningless. But Klein is actually wrong about the lack of a clear conceptual foundation for the label.
Political candidates are essentially collections of various policy positions. Parties and ideology in this sense are just associations between preferences--statistical clusters. Democrats have a certain ideological 'center of gravity' in this issue dimension space, and Republicans have a different one.
In political science, many positional theories of politics use a sort of 'median' calculation to find the ideological center of gravity. A more complex theory might add in intensity (or magnitude) to arrive at this value (mirroring an 'average' calculation in statistics). Under both theories, moderates would be considered those individuals who's ideological center of gravity is close to the overall population's. This is a fine definition that works for many applications. There is, however, still room for improvement.
Where both theories fail is in describing the set of individuals with wildly divergent collections of policy preferences who nonetheless have median (or average) statistical centers close to the big populations that we care about (the overall population, people who vote Democratic, etc.). I can support universal healthcare, radically free markets in land use, a corporate tax rate of zero and a totalitarian military-space-industrial complex and still show up as a 'leans left'. We know intuitively these people are different, but there's currently no good theory to describe them. Political science need to develop an analog to 'variance' in statistics: the degree to which one's political preferences are clustered or bunched up.