How is the sentence "This land is peaceful, its inhabitants kind" grammatically correct?
It's parallelism or, in particular, syllepsis.
It's somewhat artistic poetical figure of speech.
As to grammaticality, sure, people will look at you weird if you use it in speech. But if you're writing a novel then, sure, it's fine.
It's not a special rule of English. All languages allow this kind of parallelism. From Latin:
Fur furem, lupus lupum cognoscit.
"It takes a thief to know a thief, a wolf another wolf."