That is a really brilliant analysis. You have gone one step further into the source article and really highlighted some of its possible limitations, especially in the lack of data over a long period. Fascinating to point out how it pertains to ice cream consumption with regard to how the brain works because of the statistical evidence presented.
It is, however, important to put the findings into a wider context. Was this, for instance, a one-off study by the Institute of Psychology in London, or did they start doing research into the nutritional effects of mental health? Furthermore, sample size and diversity are likely to impact perceived reliability of the results.
It would be even more helpful to find out whether other studies have replicated these findings or if there is some common agreement among the scientific community regarding this topic. While the initial study was promising, it was only after a better investigation into the matter that any person would find any actual knowledge on the specific topic of how ice cream affects brain activity.