If you look at the definition of politics, the definition as 'The often internally conflicting interrelationships among people in a society' is the one that applies in this context. The article mentions that an individual doesn't have politics (in this sense) that affect when and why they might apologize for something. When a President is speaking to the entire world for an entire country, then there are politics.
From the article:
... what makes apologizing different for countries than for people? ... she gave me a one-word answer: “politics.”
She then elaborated: “I don’t have politics. ... But if we’re in a collective entity where there are different groups involved and we’re speaking on their behalf, and we’re in a world, by the way, where a lot of people have this idea about the kind of image we need to project to the world, then it gets a whole lot more complicated.
So, the headline is explaining what the article is about - a discussion of the way an official apology by President Obama to the Japanese for Hiroshima is affected by 'the complex or aggregate of relationships of people in society, esp those relationships involving authority or power'. Because it is a headline, most of the specific meaning of it is in the article, and not in the headline.