I just read the abstract, but it seems like interesting work. The thing that often bothers me in some studies in first-world countries is that vegetarians/vegans are probably better off than omnivores, and therefore live longer, while in poorer countries, the wealthier classes probably eat more meat.
I like that they are focusing on meat consumption, not identification as vegetarian, because the reality is that for poor people, you often eat what you can get. People often say that a vegetarian diet is cheaper, but that's not actually true. An omnivorus diet will always be cheaper; unless you think that every meal has to contain store bought meat. You could have a poor country where everyone is omnivorus, but eats very little meat on average, and a rich country where half of the population is vegetarian, but the other half more than makes up for it.
The only thing I can really point out that I don't like is that they used GDP-PPP to compare wealth between countries. That messes things up for places like Ireland where it's a reasonably wealthy country, but it's such a tax haven, you'd think it's all millionaires. There's also many countries with huge levels of income inequality, like petrostates, where most people are relatively poor, but gdp-ppp is high.
I'm still not convinced this is the right way to study the effects of meat consumption on health, but I guess it's a good part of it.