China and Korea had incredibly inconvenient and expensive moveable type that required extensive amount of labor. Page setting in western alphabet was much easier and Gutenberg invented good alloys to make it even easier. In addition Europe benefited from improved paper making technology like pulp mills (developed in Islamic world)

Just saying that Chinese had "moveable type" omits the technological and practical considerations that made European printing press success.

ps. Moveable type did bring some educational and political changes in China (centralism, opposition against government) but the effect was limited because Chinese writing system and inferior printing press technology.