Essential fatty acids (EFA) are, according to the textbooks, linoleic acid and linolenic acid, and they are supposed to have the status of "vitamins," which must be taken in the diet to make life possible. However, we are able to synthesize our own unsaturated fats when we don't eat the "EFA," so they are not "essential."
The term thus appears to be a misnomer. [M. E. Hanke, "Biochemistry," Encycl. Brit. Book of the Year, 1948.]
Current science disagrees with the obscure encyclopedia citation. Your link is quite interesting but isn't credible to me - this Dr. Peat does his readers a great disservice by mixing facts with half truths and coming to some wild conclusions. For instance, it is true that the body can assemble a variety of fats. Some, but not all. It can make saturates. It can make unsaturates. It can make w7's and w9's, it can make Mead acid, but it cannot make the w6's and w3's. Hence they're called "essential".
In the past, when the fatty acids were first identified they were called "essential" for normal growth and development. In today's science, the term "essential" has a much narrower definition. It means the substance cannot be synthezied in the body and must be obtained from dietary sources. Because some fatty acids can be synthesized by the body they are obviously not 'essential' by current definition. I think the encyclopedia excerpt is attempting to clarify this point and as such does nothing to refute what is settled science. To the extent that it names w3 and w6 as non-essential, it is simply wrong.
Again, I'd be very interested in reading something (fairly current) from a peer-reviewed journal that establishes the pathways for w6 or w3 synthesis in the human body. Perhaps this Dr. Peat has published such revolutionary research. I doubt it. In the mean time, I encourage you to read more widely and to challenge what you read by looking at the supporting science.
Here's a start: W.E.M. Lands (1992). Biochemistry and physiology of n-3 fatty acids. FASEB J 6: 2530-2536.
Another reference of interest is Mary Enig's "Know Your Fats" which is written as a primer to lipid chemistry. She also makes the case that unsaturated seed-oils are not health-promoting but does a far better job of it.