Paul Krugman is usually a very clear writer. In this article he makes some very important points but he was not very clear. I have simplified the important points that he embedded in more complex article.
The basic economic case for free trade was made many years ago by David Ricardo who explained the concept of comparative advantage. Since Ricardo, economists have proclaimed that free trade is good and that protectionism is bad. Krugman tells us that free trade does not drive global economic growth unless there is technology transfer from rich to poor countries. Technology transfer has no role in Ricardo's concept of comparative advantage. Therefore, it cannot be the sole basis for trade policy.
Krugman also thinks that putting a price on carbon is a good way to reduce carbon emissions. On the other hand administrative actions that would reduce the use of coal for producing electricity would be a huge step in reducing carbon emissions without the need of carbon pricing. In other words, there are alternatives for reducing carbon emissions that are independent from market based solutions based upon the pricing mechanism which may not have the desired impact on consumer behavior.