The severe earthquake in Italy is international news, which it should be. This is a major earthquake, and the news helps inform people. Perhaps people have relatives or friends there, and this keeps them up to date. It also shows the devastation, and relief efforts can be started and coordinated.
Any kind of big event causing killed people has to be international news. The world has to prepare for any occuring big event such as terrorist attaks or earthquake. Moreover, Italy is an important country in the world. What happened there might happen in an another important country in Europe.
Earthquakes that affect cities and that many people should be international news no matter where they occur. We develop empathy for other people in part because we see the difficulties they face. Someone may watch or read the coverage and decide to donate to help out there or somewhere else in the world or at home.
No, the earthquake in Italy should not be international news. It was a rather small earthquake. People all around the world do not need to hear about every negative event that happens anywhere in the world. Italy is too far away from the United States for this to be significant news.