Definition 4
A proposed new definition of the greenhouse theory to overcome the objections raised against warming by back radiation argues that IR absorbing ‘greenhouse gases’ hinder radiative transport from the Earth’s surface upwards and aid to keep the surface warm and warmer than it would otherwise be in the absence of those gases.
The Critique
The definition ignores the fact that those gases themselves emit radiation to free space adding to radiation loss from the system. Radiation loss to free space from the earth’s surface and its atmosphere is essentially the same with or without presence of absorbing gases for the following reasons: the cooling by radiation to free space is a one-step process; in the presence of an atmosphere, it is a two-step process with the same loss, with or without, the absorbing and emitting gaseous atmosphere. When talking about radiation, it is absorbed radiation or emitted radiation that is being considered.
I read the whole thing over at NTZ and I agree that many of the points have some merit but they are taken out of context of the complete system.
Take #4 which you quoted above. A simple analogy is a water hose. Once it is filled (!!!) then the water input equals the water output. That does not mean that there is no water in the hose, or that that reservoir of water has no function in moving water from one place to another.
We can take that analogy further by examining a hydro dam. The water input is variable but the water output is stable, with the reservoir used as a buffer to smooth out the swings in water input.
Let's compare this to the Sun/Earth energy cycle. Highly energetic solar radiation warms any spot on Earth with a sine-like intensity for daylight hours followed by no radiation in the night. The surface releases this energy by diffuse IR radiation. With no atmosphere the surface would be much warmer in daylight and much cooler at night.
An atmosphere smooths these extremes out, once the reservoir of energy is built up, like the dam or the water hose. Solar energy is stored in the atmosphere as kinetic and potential energy in the gravity field, and released in a relatively stable flow rather than the extremes that would be caused by solar input and no atmosphere.
Back to the criticism #4. Without CO2,a certain portion of surface radiation would escape directly to cold space. Instead, it is Incorporated into the total energy of the atmosphere which is constantly transforming it back and forth between kinetic, potential and radiation energies. It is not just a minor difference between a one step or two step escape. The second step is a whole complex atmospheric system that radically changes the thermal transport equilibriums.