Mr. Drigant’s grandson walked by, looking dejected.

"Looking" in this context means "appearing to be", that is, his face and his body language indicated he was sad. He seemed sad.

He looked at the cake. The cake looked delicious.

P.S. The "looking dejected" is a clause without a relative word to connect it to the main or "matrix" clause, such as "who was".

Mr. Drigant’s grandson walked by, looking dejected.

"Looking" in this context means "appearing to be", that is, his face and his body language indicated he was sad. He seemed sad.

He looked at the cake. The cake looked delicious.

P.S. The "looking dejected" clause lacks a relative pronoun to connect it to a noun in the main or "matrix" clause ("who was") because it is an adverbial-adjectival clause describing the grandson's appearance as he was walking. A relative pronoun would restrict the modifier to adjectival-only. Lacking the relative pronoun the clause can be placed at the end of the sentence after the verb; with a relative pronoun the clause could not be placed there.

Mr. Drigant’s grandson walked by, looking dejected.

"Looking" in this context means "appearing to be", that is, his face and his body language indicated he was sad. He seemed sad.

He looked at the cake. The cake looked delicious.

Mr. Drigant’s grandson walked by, looking dejected.

"Looking" in this context means "appearing to be", that is, his face and his body language indicated he was sad. He seemed sad.

He looked at the cake. The cake looked delicious.

P.S. The "looking dejected" is a clause without a relative word to connect it to the main or "matrix" clause, such as "who was".