I can see why you might be confused, but let me assure you that this is a legitimate use of the word threaten. The word threaten doesn't necessarily imply imminent violence. If you look at this dictionary entry, focus on Definition 1.3:
threaten (v.) (Of a situation) seem likely to produce an unpleasant or unwelcome result: the dispute threatened to spread to other cities
In the case of the news story, the Nigerian government is hosting of the World Economic Forum for Africa. This should be a good thing for Nigeria! However, the "unpleasant or unwelcome result" is that, instead of focusing on now Nigeria is hosting the forum, news media will be discussing this other story instead.
The word threaten is used in a similar way in this news headline:
BBC strike threatens to spoil Diamond Jubilee
In that headline, if the strike happens, something unpleasant will happen (the strike will affect the media coverage of the celebration).
It's important to note that is wasn't the strikers who were threatening the Diamond Jubilee, but the strike itself. (Had the strikers issued a threat, that would have implied something different – something more deliberately disruptive.)
The word begin could also have been used in the sentence, as you did, but the meaning shifts a little bit.
The fact that our mother is in the hospital threatens to ruin our Christmas.
The fact that our mother is in the hospital has begun to ruin our Christmas.
In the second sentence, the unpleasant event is already underway – Christmas is being ruined as the speaker says his sentence. In the first sentence, however, a ruined Christmas isn't necessarily inevitable. There's still time to count our blessings and ward off the threat of a ruined Christmas.