You're confusing first world with western world here. And you're confusing the Cold War's spheres of influence with culture.
Maybe Americans see themselves as being Western now, but in the way it used here, that wouldn't make sense. Besides, I'm European, I've been to the US twice, I get more than enough news from the US: there are substantial differences. England has always been a weird case in Europe, they are islanders, and is probably part of the reason why they will leave the EU. If that's the case for the English people now, then how would be the mentality of Anglophone people who have to go back centuries to find their English descent?
The Balkan culture will be renamed Nation States, or something like that. They will represent the other, minor countries that were in Europe, mainly in Eastern Europe. That would mean that Russia should not be part of this culture.
Why are the Brits not in the Anglophone culture? Well: 1) Vanilla decided they are European 2) They are culturally very close to Europe 3) the Anglophone culture in this mod represents the English territories, or territories who somehow gained English as their first language.
Why are the Ottomans in the European culture group? Well: 1) Vanilla decided they are European 2) Their politics were heavily focussed on Europe. Even the capital was in Europe. 3) They aren't exactly like the Middle East. Most likely because of 2.