Actually a Gutenberg press would work totally fine for Chinese characters. The problem is not the press but the creation of punches. The Chinese system relied on wood carving which is relatively fast to create a punch which you press into clay to create a mould to cast your types.

Gutenberg used steel punches which are knocked into copper to create a mould. You got to create a punch for every character and that is very slow. Cutting a hard metal like iron is slow. They calculated Gutenberg needed a year to make the whole alphabet, only 24 - 30 characters. Doing the same for Chinese characters would easily take a century. Not practical.