It sounds like any of the algorithms for extractive summarization, like LexRank would apply. You should be able to pick the most meaningful sentences of a news that way and then only classify those, without a  seperate class for “other”.
Of course there is no guarantee that you won’t exclude sentences that shouldn’t be in the “other” class.
Another thing I would try is to classify anything as other, that doesn’t have very high probabilities for the rest of the classes. So if your model outputs a low probability, even for the highest-probability class (i.e. it’s not confident in it’s prediction), just treat that as “other”.