First off, this is not Jade Empire, although I think it was out at the same time, and was probably looking for the budget market for aficionados of the aforementioned. The main character is a muscular Asian man, I believe, probably dressed in red, some sort of martial arts robe.
Levels involved movement with the keyboard, and attacking with the mouse, I think. I do remember that there was an attack button and a counter button. I never quite got the hang of countering, although I'm pretty sure it was necessary to really advance in the game. Most enemies were generic martial artists, monks perhaps, but occasionally you'd fight someone at a higher level, and they'd generally mix magic and throwing fireballs around. At least one level involved being confined to a rooftop against the boss, only able to move left and right. I think that's where I got stuck, as that level really required you to be pretty good at countering.
You got a score, and a grade, at the end of each level, I think based on speed, avoiding getting hit, and some other factors. I want to say the grades showed up as scrolls.
I believe I played this game in the early 2000s. I definitely played it on the PC, but it might have been either Steam or Desura. I'm 90% certain I got it in either a Humble Bundle or Indie Gala.