Here's the thing: the chart the writer provides is actually pretty good. It does a simple outlining of the different schools within the science of economics. While I don't necessarily like setting up categories like this (you could just as easily make 4 categories as you could 20 with roughly the same degree of legitimacy) it's a decent enough summary of those popular disciplines that are different enough to be notable but not so overwhelmingly detailed about each one's nuance.
What I had an issue with is his introduction to the piece, adapted from a book by Ha-Joon Chang:
Despite what the experts want you to believe, there is more than one way of ‘doing’ economics
People have been led to believe that, like physics or chemistry, economics is a ‘science’, in which there is only one correct answer to everything; thus non-experts should simply accept the ‘professional consensus’ and stop thinking about it.
Contrary to what most economists would have you believe, there isn’t just one kind of economics – Neoclassical economics. In fact there are no less than nine different kinds, or schools, as they are often known. And none of these schools can claim superiority over others and still less monopoly over truth.
Of course, where economists differ (and where the above schools of thought come into play legitimately) is when we get into the massive transactions that make up a global economy. Of course, it's a tenet of most classical economists that there is no way to track all of this (nor would we necessarily want to), and so the best thing to do is let the invisible hand (or, according to the chart above, eight other different theoretical things) sort the whole thing out. The degrees in which various institutions and macro-level decisions are made make up the differences in how the various schools of thought view the economy.
Really, however, any economic "school" that rejects the fundamental, nuts-and-bolts foundation of economic thought (like, say, supply and demand) really can't be thought of as economic systems, but (as my experience has seen) should be considered political ones. (Or, if you prefer, "social.") That's why I don't consider the sort of surface-level Marxism that most so-called modern-day socialists and communists adhere to really isn't an economic system at all, but rather a way to use brute force to change the laws of economics to fit political ends. (I say surface-level because, throughout its development the last century or so, many intellectual Marxists have made legitimate (if, in my opinion, erroneous) attempts at reconciling Marxism with the commonly accepted laws of economics.)
Why point all this out? It's a disturbing (albeit in no way new) trend to see people reject blatantly obvious economic rules to fit some sort of agenda. You can't simply say "Oh, the cost of health care/minimum wage/etc shouldn't go up because, well, it shouldn't" and completely ignore the fact that there's quite a few centuries' worth of evidence to state that we can't simply ignore the side effect we know full well is going to occur simply because it "shouldn't."
We wouldn't expect a glass jar to not fall off the table and shatter because it "shouldn't" have been dropped, so why would we expect the price of something not to rise if we artificially restrict its supply, simply because we think it "shouldn't"? Perhaps it should be the role of the government to "fix" it--in fact, there's quite a few reasons why we might want to do just that-- but let's not pretend it's not going to happen in the first place, and we need to acknowledge that adjusting the economy to fit political needs is going to have a hard cost involved.
So Chang is kind of right in the sense that there is "more than one way of ‘doing’ economics." However, I reject that the foundations of economics are any less solid than the foundations of chemistry or physics or biology. Sadly, many people do.