I don't really think Chinese chariots was some invention that came from the Middle East. Chariots from different countries like Egypt and the Hittites, were different among themselves, reflecting differing military doctrines. The Hittites for example, preferred their chariots heavier and bigger, where you can put more archers on it, while the Egyptians go for lightweight, speed and maneuverbility.
The Chinese chariots seem unique on their own and don't carry specific influences from the Middle Eastern empires. Would have been difficult for any chariot to transverse across central Asia in the first place.
The chariot itself was the militarization of a rather popular and mundane vehicle that is typical of sedentary cultures, the wheel cart. Anyone who had the wheel cart would inevitably have chariots.
The concept of pure cavalry on the other hand, came from the Huns. They were first encountered and fought by the Zhao, and later the Zhao would use all cavalry formations against the other Warring States. By the end of the Warring States period, chariot use had declined to the point they are mainly for pageantry and as a command vehicle by the top generals.
From Han later on all the way to Tang, the cavalry dominated and was the golden age of cavalry in China. The stirrup began mass manufacture towards the end of the Han Dynasty, just in time to be used in the Three Kingdom wars. From the Three Kingdoms to the Sui, cavalry was increasingly armored, and this was the period in China where it came closest to having the equivalent of knights, or heavy cavalry. Turkish influences on the Tang changed this again, and the Tang went for the speed of the light cavalry.
Chariots, or to be more precise, wheeled carts, later returned to military service but not in the manner people thought. With the invention of fire arrows, mainly rockets with arrow tips, came the invention of multiple firing boxed launchers, a sort of prmiitive MLRS. These were often mounted in wheeled carts, creating an early artillery battery.
Evolution of swords in China also reflect foreign influences. Up to the Warring States period, the predominant sword form was the Jian, straight blade with two edges. From the Han on, this changed to the Dao, which is a single edged sword. The change from Jian to Dao reflects cavalry use, and the change of swordmanship from thrusting and stabbing attacks to slashing. But later on the Turkish and the Mongols influenced the Dao design to a curved saber form, starting to appear by the Yuan and Ming Dynasties.