Q: Why does the article include the name in Spanish at the top?
A: Because as this article talks about a sovereignty dispute, and the name is part of that dispute, both ones are referenced in the lead. The rule is to name the islands as Falklands, with a reference to the Malvinas name on first use in the article, and from then on call them simply Falklands. This rule is detailed at Wikipedia:Naming conventions (geographic names)#Falkland Islands. This rule only apply to articles that deal with geography or the dispute itself.
Q: The newspapers are talking about the dispute! Shouldn't the article include that info?
A: In most cases, the likely answer is no. This article tries to keep a summary of the dispute from a historical point of view, and avoid recentism. Most of the times that the press talks about this, it is either the anniversary of some old event, or something that can be shortened as "A British politician said that the Falklands must remain British" or "An Argentine politician said that the Falklands must be Argentine". Those things rarely have an actual significance for the dispute, as they are just a confirmation that both sides are simply staying at their regular positions. Sometimes, a modern event may have the required historical significance (such as the Falkland Islands sovereignty referendum, 2013), but those are rare, and do not take place on a regular basis.