If so, it should be 수프를 as 좋아해요 is transitive.

Technically, yes, but 좋아요 is often used in speech to, more-or-less, mean the same thing as 좋아해요. 좋아요 translates to "to be good", so this sentence should be translated as: "Salty soup is good." The implication is that you like it.

If a friend asks "Do you like this movie?" and you nod and say "It's good!", they would probably be right to assume that means you like it. I'm not sure if this applies to the written language in Korean, but in spoken it seems quite common.