China’s Kweichow Moutai Co. has become the world’s most valuable liquor company thanks to a fiery spirit that can cost nearly $400 a bottle.

The spirit is baijiu, a Chinese liquor made by fermenting sorghum or other grains in brick or mud pits. The company’s version, known simply as Moutai, has a long association with China’s Communist leaders, and has become a homegrown status symbol for affluent Chinese.

One...