You are right, it is hard to explain. However, I for one think that this is a bit over the top (I am dutch as you may know, so this is a different perspective than most of you have). I will do my best to explain why I think that it is fine as is.
Zwarte Pieten are part of the celebration of Sinterklaas and are the reason that Sinterklaas is capable of delivering all those presents. Zwarte Pieten are the ones who make it possible. Much like the elves of Santa. They also do all the work, except for the delivery of the presents, which Santa Claus does himself if I am not mistaken. You cannot say that Santa Claus is racist because his helpers are all elves. Maybe the trolls also want to help, who knows?
My point is, the Zwarte Pieten are the elves of Sinterklaas. They help him to complete the monstrous task ahead of them. Dutch children see Zwarte Piet as American children see the elves of Santa. As the helpers who make everything possible.
And even if it is a reference to black people, I do not see how it is a problem. They deliver presents, are nice to all people and make people happy. I don't see the negative association to be completely honest.
This is pretty much what I have to say about Sinterklaas en Zwarte Piet. Now I will place it in context with a rant about political correctness and racism.
We have a tendency in the Netherlands (and the rest of the western world) to remove everything which could be remotely interpreted as racism. Everything has to be politically correct. For example, Angel Kisses, formerly known as Negro Kisses in English. In the Netherlands, we called them "Negerzoenen" until 2005. In 2005 they decided that "Zoenen" was a better name, because it was more politically correct. However, we still have "Jodenkoeken" (Jewish cookie) and "Blanke Vla" (White Custard). Those aren't politically incorrect for some reason. I think that it is because those have nothing to do with black people. Jews? No problem, they don't complain. Whites? Ah, they are the majority. They can take it.
What I see is that black people (and jewish people to some extend) are treated differently. And here I am, thinking that treating someone differently because of race is racism. What we are supposed to do is leave race out of the equation entirely. It is like men and women. You have to leave gender out of the equation entirely if you want true gender equality. It is a lot like gender equality actually. You cannot make people equal by forcing a quotum of "non-whites" or females on a company or public body. It just does not work. All it does is make people more aware of the differences between people instead of less.
EDIT: After reading the article again, I saw that they actually linked to GeenStijl. Let me clarify: GeenStijl is a blog which makes money with Schadenfreude and satire. It cannot be taken seriously, just like you cannot take 4chan seriously.