Yes, Dickerson does point out that his exponential fit is a linear relationship on a log scale. For example, he does show a log-scale in figure 3 (pg3), fitting the most reliable 83 nation-points on a plot of log(GDP) against mean IQ in which the exponential fit looks exactly like you would expect. (Is it per capita? As far as I can tell, he always means per capita GDP even if he writes just 'GDP'.) Figure 4 does the same thing but expands the dataset to 185 nations. The latter plot should probably be ignored given that the expansion comes from basically guessing:

In their book, IQ and the Wealth of Nations, Lynn and Vanhanen (2002) present a table listing for 81 nations the measured mean IQ and the per capita real Gross Domestic Product as of 1998 (their Table 7.7). They subsequently extend this to all 185 nations, using estimated IQs for the 104 new entries based chiefly on IQ values for immediate neighbors (their Table 8.9).