The indirect object in this sentence is the word mess.
There are two objects in this sentence, and those are room and mess. However, the first object in this sentence 'room' is a direct object, not an indirect one. You can easily check this by asking the question 'what.' What did Luis once leave a mess of his own? - Their room. This means that the word room is the direct object, which leaves us with mess as the indirect one.
