"A man who does not drink"
Translation:마시지 않는 남자
It's actually not a topic particle, it just happens that conjugating a verb to make a relative clause often looks like one. This is the phrase "the doesn't-drink man". It's actually more convenient than English, because in Korean, descriptive phrases come on the same side of the noun as descriptive words (adjectives, like "tall") do.
The "drink-not" man. The "---는 " here is a different thing from the particles used with the other subject topic lessons. Same spelling, different purposes.
Here this one changes verbals to descriotive that act like adjectives. And that includes negative like this phrase.
Descriotive verbals just like in English adjectives must be in front of the noun.