From the article:

It also appears that the authors fall prey to statistical illusions. "Creaming curves" are published for some regions, where the fields, when ordered by size, appear to yield an asymptote which is interpreted as evidence of an approaching limit. But ordered by date of discovery, the asymptote is not as clear, as Figure 1 shows for the UK. No explanation is given as to why ordering by size is more appropriate than by date of discovery, and in fact, the asymptote appears to be nothing more than a statistical artifact--that is, use of a large population, ordered by size, will frequently yield an exponential curve with an apparent asymptote. This is especially true of oil and gas exploration, where basins usually hold many more small fields than large ones

In fact, Lynch is criticizing the Parabolic Fractal Law that has been studied by Jean Lahèrrere and not the actual "Creaming curve" shown on Fig. 2. However, the PFL is quite a general phenomenon that has been applied with success in many different areas (Astronomy, Geology, biology, internet traffic, etc.) and is a simple variant of the Pareto distribution. I don't think he really understood Lahèrrere's approach.
Lynch is another one whose bread is buttered by those who fear that awareness of limited hydrocarbon resources will lead to higher or new taxes on the exploitation and use of those resources.  Thus he may well have understood Laherrere's approach, but chosen to misrepresent it.