viz.

I disagree; I think the cover is quite humorous.

What Siegel and many other commentators seem to have missed is any discussion of audience. In the quote above, Seigel repeats one of the major complaints about the cover, namely that it is going to reinforce these stereotypes of the Obamas. But I find this claim ridiculous. What reader of The New Yorker would think that an image as exaggerated as this one is meant to be taken seriously? It is pure hyperbole. The New Yorker regularly contains sophisticated humor, something that its readers could be reasonably expected to be aware of and prepared for. I would be very surprised if any sizable number of the magazine’s readers needed to have the satirical intent of this cover explained to them.

That is not to say that everybody gets it. Of course there are going to be people who would misunderstand this joke. (And in this group I’m not including those who have no sense of humor.)

Further, I would say that all satire wittingly reproduces whatever slur or misconception it targets for the express purpose of demonstrating that said slur or misconception is ludicrous, an emperor with no clothes. Without repeating the slur—usually in a slightly modified form—it wouldn’t be satire at all.

As you point out, there is a lack of context on the cover. However, I believe the magazine and its audience provides the necessary context for understanding the intent and target of the joke. I think you would be hard pressed to demonstrate what it is in the image that is satirizing the Obama’s themselves, rather than satirizing the rumors and lies that have been spread about them online. The reason I think this is the case is that the image only mocks what others have said about them, not any of their own foibles.