That dog gets fatter every day is written correctly because it does not contain a combination of two superlative adverbs or two comparatives. It only contains the comparative form of the adverb fat.
However, a close study of other options shows combinations of two superlative adverbs in the same sentence. For example in option A there is most (superlative form of much) and loudest (superlative form of loud) in one sentence. The same situation plays out in option D where most (superlative form of more) and quickest (superlative form of quick) exist together.
On the other hand, there is the existence of two comparatives in option B as more is the comparative form of many while fuller is the comparative of full.
