The title of this study isn't representative of the tests they actually ran. It falsely lumps together flat design and a terrible design hierarchy, which is expressed by the strategic use of contrast and color.
Further, some of the tests aren't representative of an argument for or against "flat" when they compare [a bright pink button with gradient and drop shadow] to [a white button with a light gray border], both on a mostly white page. Of course people will see a fat blob of pink faster than a faint gray-on-white, regardless of any drop shadows or gradient effects on either of those items. That's an absurd comparison if you want to make a point against "flat ui".
If you want to compare flat vs. non-flat, you better use the same pink button in both cases (or the same faint gray button) - once with and once without any effects such as drop shadows or gradients.
This study is very one-sided and merely confirms what any designer worth their salt already knows: you need to make actionable elements stand out from the rest of the content, plain and simple. Contrast is king, no matter if you're making a flat design devoid of any depth or if you're using drop shadows and rainbow gradients.