It was 'won', of course, only in terms of power, but it is worth noting that the thing which won was not classical liberalism but the heavily modified Keynesian capitalism of the post-war era. And even that only 'won' because in the West the well being of the lower half of the population is not a criteria of evaluation.
Indeed, the western economic model, whatever you want to call it, generates much more wealth, which is almost always equivalent to power. Indeed the core of "classical liberalism" isn't at all what the west has now or had then, but we do have much more economic freedom/less economic restrictions/regulation than the USSR etc. did.
The lower half of the population in the west is also much better off in absolute terms than the lower half of the population in other parts of the world, much more so than the lower half in the Soviet Union and China was then or is now.
