Well, strictly speaking, Korea, Japan, Vietnam, and Indonesia were other cultures that cast their coinage

I think Rome was the only other one to start out casting all of their coinage, since the aes rude, aes formatum, aes signatum, and aes grave mostly all predate their struck silver and gold by several decades to a century.
Olbia dolphins were cast, although I am not sure if they were the only coins at the time... and certainly aren't round!
The Sunga kingdom did cast most of their coinage, but IIRC they continued making punchmarked coins as well.
I'm not terribly familiar with Celtic potins, but I think their gold and silver were struck at any rate.
The earliest "coins" (marked ingots) of Sri Lanka I believe were cast, and the later massa coins produced locally were also cast (though gold and silver may have been struck).
As the Tang dynasty became the major financial power of the world, several kingdoms in central Asia abandoned struck coinage to make cash coins of a local flavor.