It is necessary. Without "hơn", the sentence no longer has the sense of comparison, in which this sentence's meaning arguably remains unchanged. You are not recommended to apply this (ignoring "hơn") in other cases.

And try not to literally understand them. Evidently, most Vietnamese sentences sound weird in English.

It'd become „eat little, think a lot“, I presume.

You don't need " than". You just write "Eat less think more

That's not a grammatical sentence in English. You need a verb... "To eat less IS to think more". And even then, it's not a good translation. The VN sentence is an imperative, whereas the sentence you gave is not.