I can't think offhand of any Asian directors who have done adaptations other than Kurosawa. Though I would be more surprised if there weren't others out there.

An IMDB search of plot summaries on "Shakespeare" and various Asian countries only produced one that sounded like a contender:

Qing ren jie (2005)
us.imdb.com/title/tt0450099/

Here's the very badly-written IMDB plot summary:

"A love story that should not have happened. But the Great Cultural Revolution fathered it. As memorable as Romeo and Juliet, their love tied with the same intrusion from their families ¨C the hatred. Until one day, they watched Shakespeare's Romeo and Juliet. It inspires them. It gives their juiceless love story the hope for fruit. It brings them the determination to bridge through time setting aside the hatred. The same gives them a wait of 12 years. 12 years of changing time, changing era. Friends come and go. Songs sang become old. How much longer for their love can they hold? How much longer for their love with beautiful memory and unforgettable days can they hold?"

anyone seen the Feng Xiaogang movie the banquet? its suposed to be hamlet