China Warrior is just a Kung Fu themed port of the arcade game Gladiator. I don't know if the same staff worked on both games, but they're exactly the same, except for the attack moves.
You can play Gladiator on Taito's classics compilation for PS2 and Xbox. It's one of the best retro sets around and is a must buy for Plump Pop alone.
Gladiator's one of the beloved arcade games from my childhood and I've been sitting on the pcb for years, but it's not jamma and I'm not electronically inclined. But the Taito set makes up for it.
If were to name the genre China Warrior and Gladiator fall under, the best title would be to call them "Garbage Storm" games, since both involve you walking into the wind as a pile of junk gets tossed at you again and again.