A first fix, shown on the left below, puts the two data series in a scatter plot. If one accepts the existence of a linear relationship between 2004 installations and 2004 stock, one would be mistaken indeed as such a comparison is meaningless; for countries differ significantly in terms of the number of robots deployed (Japan has over 300,000 while many other countries have fewer than 1,000).
A second fix substitutes the 2004 growth rate for absolute number of installations. It is now clear that the growth rate is not much associated with the size of the installed base, contradicting the perceived linear relationship from before. (Note that the x-axis is plotted on a log scale.) The European countries are shown in red, most of whom have grown their stock of robots at a higher rate than Japan.
In order to highlight the Europe/Japan comparison, one can plot the European average, rather than individual countries. The message is less murky because the graph is less busy. The following set illustrates this. What really stands out from these graphs is China (& Taiwan), not Europe. Incidentally, China was omitted from the Economist chart, which is a rather mischievous deletion -- but is understandable since China's data is hidden when they used the original data series of installations versus stock (green text on the left chart).
Reference: Economist; United Nations Commission for Europe
I'm writing this from a different computer while I'm travelling and I'm having trouble with the tools at my disposal. Apologies for some glitches in the charts.