This map clearly does not include enough of Europe, and too much South America and Africa. So, let's try adding a lot more Europe into the mix:
Horrors! Even more of Africa is included in that definition. No, what we really mean when we say "West" is a map that looks more like this:
So when you see the word "West" you should read it as "white." This is what we really mean. It no longer has anything to do with an actual geographic direction, although it did at one point before the New World got thrown in to the mix. The simple fact that it's inaccurate isn't such a big deal. There is a generally accepted definition which is accepted and understood by the majority of folks.
What I do have an issue with is the exclusionary attitude toward world history/culture/literature/whatever that this creates. The focus of so many discussions becomes the East/West divide, because this is the language we like to use. Unfortunately, when West means white and East means Asia, you end up with a world map that looks something like this: