Well, it certainly makes sense to keep track of the number of free parameters in a theory. If you can find another theory which fits the data as well and has fewer free parameters, it's superior and you've made progress.
However, the counting he does in Table 1 is complete nonsense. It's just totally wrong. He seems to be pretending that each of the experimentally determined values he lists in column four are
single measurements. But that is absurd - each of those values is determined from thousands, millions, even billions of measurements. One only needs a tiny subset of those to determine the relevant parameters;
all the millions of measurements that remain are checks of the theory!
Think of it like this: you have some set of data which you keep in a box. You have a theory that seeks to explain that data. All theories contain some parameters, so you have to pull out some data from the box and use it to fix those parameters. Once the parameters have been fixed your theory is unique and makes predictions for everything remaining in the box. If it agrees well you're happy, at least until you find a theory which does as well with fewer parameters. Ideally, you only need
one single data point to fix a parameter! In practice it's better to use an average over many measurements to reduce the effects of errors and other uncertainties, but even then you're only using 1 number (it's just that it's an average). All the remaining numbers are checks on the goodness of the fit of your theory to reality.
In this case, how much data do we need to fix those cosmological parameters? Let's pick 1: H_0, the Hubble constant. We can determine H_0 in many, many ways, and that's the point. We pick one way - for example, we measure the average redshift-distance relation for some set of standard candles - and then we make sure our answer is consistent with all the other ways we could measure it. And even within the set of standard candles (say, type 1A supernovae) we make sure that they are all in agreement to within some reasonable errors (from peculiar velocities, measurement error, etc.). So in the end we used 1 number to fix H_0, and then we predicted (or postdicted) literally
millions of data. Counting all that data as 1 measurement is just
totally wrong.
By the way, there are mathematical formulae, which are occasionally used in hypothesis testing and theory comparison, which formalize what I said above. If this guy were serious he would have used one to do this analysis, rather than this ridiculous "significance". But the answer would have been overwhelmingly against his (plainly) forgone conclusion, so I assume that's why he didn't.
