I just had a very quick look-through of Y&G, but it looks like they tested for curvilinear (i.e., a log transformation of GDP) only. I could be missing a footnote, but I don’t believe they included a second-order GDP term to test a polynomial relationship.
However, the findings of the 2013 paper largely support that, from my quick reading. The estimation of the second-order coefficient is significant but basically zero for most of the different data slices. Further, when they back out the inflection points, the income levels for the turning point of meat consumption are much higher than the turning points for other Kuznets curves ($45K relative to $3K-$12K in the general environmental KC literature).
But actually now that I’m digging in to the results, I think the tables report different numbers from the text. Neither Y&G nor RC&M are forthcoming about their units, which is frustrating, but at least Y&G discuss their results clearly. I’m a bit frustrated about the write up of this paper. I believe that you’re reading the results correctly, unless the authors are actually using per capita GDP in thousands like Y&G and failing to report that (although that result wouldn’t make any more sense). It does seem a lot higher than Y&G.
I’m losing faith in this paper now (at least in the result discussion), but I would like to check out the literature further and see if there are any other newer papers that can provide insight into the differences.