This is the 655th most frequent Korean word.
없다고
"없다고" means "saying that (something) does not exist" or "saying (someone) does not have."
In this sentence, '없다고' conveys reported speech, indicating what he said about his absence from home.
그는 집에 없다고 말했어요.
He said that he is not at home.
Here, '없다고' reflects the reported reason for the lack of time given for not keeping the promise.
시간이 없다고 약속을 못 지킬 이유는 아니에요.
Saying that you don't have time is not a reason to break a promise.
In this example, '없다고' is used to report the children's statement about the absence of fun games.