Second order thinking would be thinking about processes, rather than the situation.
So if you have a problem like in the article, you don't like the current government. First order thinking is fund the rebels. Second order thinking is thinking about which countries have had good outcomes from government change and which countries had bad outcomes, which countries had a gradual power turn over, which countries end up friendly to you. By quantifying what outcomes are most favorable and finding out the prerequisites, we can then formulate a policy that is consistent for many cases.
Then you can eliminate first order thinking, since you have already done a better job in the general case and you can clearly see funding the rebels is far outside the parameters of your general policy, so it's a waste of time or worse.
So if you have a problem like in the article, you don't like the current government. First order thinking is fund the rebels. Second order thinking is thinking about which countries have had good outcomes from government change and which countries had bad outcomes, which countries had a gradual power turn over, which countries end up friendly to you. By quantifying what outcomes are most favorable and finding out the prerequisites, we can then formulate a policy that is consistent for many cases.
Then you can eliminate first order thinking, since you have already done a better job in the general case and you can clearly see funding the rebels is far outside the parameters of your general policy, so it's a waste of time or worse.