My guess (not 100% sure) is DLG wants to highlight the meaning of the suffix "-지". It is a clause nominalizer that transforms the attached clause into a noun-phrase/phrasal noun (or gerund phrase, in English).
(1) [... 은/는] 많지 = a lot [of ...] (noun)
않아요 = it is not
많지 않아요 = It is not a lot
▪찬장은 많지 않아요 = Lit. Speaking of cabinets, it is not a lot => There are not a lot of cabinets (by inference)
(2) 많이 = much/many; a lot of (adverb)
▪찬장은 많이 없어요. Lit. Speaking of cabinets, there are not many. There are not many cabinets
(3) 별로= (not)particularly; not really (adverb, downtoner for negative sentences).
▪별로 찬장은 없어요./찬장은 별로 없어요 (별로요). There is really no cabinets.
▪별로 찬장은 많이 없어요./찬장은 별로 많이 없어요 (/많이 별로요). There are not really many cabinets
▪별로 아무 찬장도 없어요./아무 찬장도 별로 없어요 (/별로요). There are not really any cabinets.