Per country emissions is a terrible measure, because the atmosphere doesn't care about country boundaries. For accessing whether or not a country is doing its share to address the problem, per capita emissions is a much better measure.
The atmosphere cares even less about per capita than per country. It doesn't care about whether we "do our share" either.
You specifically called out China for high emissions. If you measure per country, then if China were to split up into several smaller countries, all of which keep the same per capita emissions, by per country they would all be low emissions countries. That nicely illustrates the absurdity of per country.