In my view, rigidities exist in the real world and to describe accurately how the world works you need to incorporate such rigidities in your models, which of course Keynes emphasized. But you also need to include forward-looking expectations, incentives, and growth effects--which Keynes usually ignored.
In my view the essence of the Keynesian approach to macro policy is the use by government officials of discretionary countercyclical actions and interventions to prevent or mitigate recessions or to speed up recoveries. Since I have long been critical of the use of discretionary policy in this way, I think the Economist is correct so say that I am anti-Keynesian in this sense of the word.
What I call the textbook Keynesian model is one in which you think of everybody as working in a GDP factory, and the aggregate price of labor is fixed. (If you go to the graduate textbook model, you have prices that move, but too slowly, and it can have stickiness in output prices, not just the wage rate.)
In terms of theoretical outlook, I would say that anyone who works with the GDP factory model and the textbook version of aggregate demand and aggregate supply is conducting the conversation in a way that is understandable to the Keynesian tradition. However, there are those on the far left and far right who do not like the GDP factory story and who see things as more complicated.
Some of the "it's complicated" folks are on the left. I think of Minsky, or Akerlof and Shiller in Animal Spirits. These folks advocate Keynesian policies, but without the pretense of mathematical precision that one finds in textbook models.
Then there are the "it's complicated" folks on the right. As I have thought about these issues, I find it less and less plausible that the dominant reason that the economy departs from the full-employment idea is stickiness of nominal prices. There are so many other things that need to change in a dynamic economy.
Is Borders Books going to be closing down and letting go of 10,000 workers because of lack of demand? Yes. But is the problem a lack of aggregate demand, meaning the ratio of the money supply to average prices? I would say no.