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I tried to parse it by reading the intro and the conclusion. Is it trying to say some of the heating effects will be potentially saturated and limited when co2 increases, decreasing temperature? York and Princeton seem legit but don't know about how well received this is

They're saying "The effects of the first ton of CO2 dumped into the atmosphere is much higher than the effects of the next ton. Now there's so much CO2 in the atmosphere that dumping any more into it will have a negligible effect."

The implication is "There's no need to worry about CO2 at this point, it's already done the damage it can, so let's call our global warming concerns off". But the models may be suspect (see my other post), so I wouldn't go celebrate just yet. Let's at least wait for peer review or submission to a notable journal to see how well received it is.

The essence is that each frequency alone is eventually saturated. (can't absorb more than everything). If you add more CO2 you'll start to absorb more in new frequencies, but the effect is getting smaller. To calculate how much the numbers add up, there is HITRAN-Database with a lot of data about the absorption lines.

About these calculations there's interesting material out there. I think there's even software to download, and feed with a download of HITRAN-Data.