"Government" in this case refers to the Prime Minister and his cabinet, not to the state as a whole. The article says it was a "coalition government," meaning that no one party has a majority in Parliament, so a coalition of parties worked together to elect a "government."
"Government collapse" just means that the guys in charge lost the support of one or another of the parties that elected them. They've got to hold elections, to see who will be the next Prime Minister, Foreign Minister, etc. It's not as big a deal as it sounds like to our American ears.