The timing is interesting. According to the article, one of the reasons this did not succeed more broadly was due to the large number of characters in the script adapted from the chinese writing system. The invention of Hangual a couple of centuries later did bring to Korea a script with dozens of letters instead of thousands. If the modern script was invented first, perhaps we would be crediting Korea as the birthplace of the printing press.
Hangul is still quite finicky to create a movable type with though. Although the basic letters themselves count in the dozens, they can combine not only horizontally but vertically (and even both at the same time), so in practice you would have to create every block for each possible syllable. It's still a lot less than the Chinese scripts, but large enough to make the printing press less practical than the alphabet. (Here's an example of a Hangul movable type: https://www.museum.go.kr/files/zin/curator_14_3.jpg)
edit:fixed typo