I think it's more a question of degree, Europeans were also obsessed with ancient Egypt[1] at the same time. But that faded away, where Japanese culture has retained its appeal. Of course, ironically anime are full of medieval European-esque knights and wizards and elves, so the draw of 'exotica' is widespread.

1: https://en.wikipedia.org/wiki/Egyptomania

I suspect part of it is that China was so cut off from the rest of the world for so long over the last century. When I was growing up through the 70s and 80s, and even the 90s the only asian culture you got exposed to was mainly Japanese culture and Hong Kong movies. Mainland China was a cultural black box. Even the Chinese culture we did have access to, like "The Water Margin" and "Monkey" TV shows were Japanese productions.

I also grew up in that era and the other part worth mentioning is that Japan seemed to be taking over the world economically. Japanese cars rapidly replaced American cars on the landscape, Japanese electronics did the same. Japanese money was said to buying up the entire country.

It was pretty natural to fetishize a culture that seemed so staggeringly successful and ascendant.

I think Japan cultural was/is seen as both ‘untainted’* due to their historical isolationism and the ability to mostly resist foreign encroachment and sufficiently sophisticated enough not be considered inferior which makes it pretty unique from the western perspective.

*of course modern Japanese society is probably much closer to Victorian Britain than to what Japan was in the 1850s