> So what does it mean? What was the goal of collecting the data? What would the interpretation have been if the data would show a significant positive effect of Theanine?

I think what the author is saying is that for them to bother with theanine on a permanent basis, it would have to have shown an effect large enough to be apparent just from plotting.

In other words, they mean technical significance as opposed to clinical significance. A small effect can be statistically verifiable without being meaningful in practice.