Does 만석꾼 (萬石君) mean "a king with 10,000 stones"?

 ANSWER: No!

The Chinese character 萬 (만) means "ten thousand," 石 (석) means "stone," and 君 (군) means "king," but 石 can also mean "a straw bag," the kind used to hold rice, and since 君 can also mean "man," the phrase 만석꾼 (萬石君) means "a man with 10,000 bags of rice," which means the man is "a rich man." 

My Korean-English dictionary defines 만석꾼 (萬石君) as "a rich man," "a millionaire," and "a person who owns fields yielding 10,000 seong of rice."

From Dong-A's Prime Korean-English Dictionary

There is also the word 천석꾼 (千石君), which means "a man with 1,000 bags of rice." A 천석꾼 is also "a rich man," but not as rich as a 만석꾼.

The following proverb uses the words 천석꾼 and 만석꾼:

천석꾼에 천 가지 걱정, 만석꾼에 만 가지 걱정

"A man with a thousand bags of rice has a thousand worries; a man with ten thousand bags of rice has ten thousand worries."

The proverb suggests that the more assets you have the more worries you have.