Dienekes labelled the admixture "West European" because that was where it was more commonly found today
(in fact he should have called it "North-West European"). There isn't a sequence in the DNA that says "West European" in it ! We call it whatever we want. The point is, this particular admixture was probably found in northern Anatolia a long time ago, but the people migrated, and it is now found most in North-West Europe. You should think this way for every admixture and every haplogroup.
It's easier to think only in modern terms, but it is mistaken. Most people think like you, and that is why most people originally thought that R1b was associated with Cro-Magnon, and why many people now think that R1b came with Neolithic farmers. It's not that easy to redraw the map of population movement through the ages in one's mind.