Well, it *is* meant to be satirical; that much is obvious. One of things that bothers me most about that photo is that they dressed the kid in fatigues and boots; he is meant to look like a small soldier. The fact that the mom is really tall and thin and looks like a professional model makes the whole image look like some sort of short man's sexual fantasy.
The topic of the article is Dr. Bill Sears' attachment parenting philosophy. The thing is, I was a fan of Sears' from way back, though I'm not a slavish follower of any particular philosophy. (My liking for attachment parenting came from the convenience factor. When it stopping being convenient, then it lost value to me.) While Wm. Sears does advocate extended nursing, he isn't nearly as controversial as his son Jim is. It's the son that has pushed the limit on the uber-mom philosophy, and who is anti-vaccine. Based on what I know of the elder Sears, he probably is rather unhappy with the exhibitionist philosophy implied by that cover.
I'm fine with extended nursing, and my youngest didn't wean until she was close to three (she weaned by my choice, BTW, not hers; I have my limits.) However, every Western woman who I have ever known who practiced extended nursing began to set limits on it by the time the child was verbal, and made it very clear that it was a private-time thing that would be limited to certain circumstances only. Once a child is fully adapted to solid foods there is no need to nurse on demand, nor should you, because they need to learn limits on it just the way that they learn limits on everything else. No one I've ever known would have allowed a child over age 2 to nurse in the way depicted in that photo. (As to the benefit, it's primarily emotional for the child. In my case, the primary benefit I got out of it was weight control, which was a nice side benefit, but not a compelling reason to continue.)
PS: As to the age of the child in the photo, before I read a bit more about the people in the photo I would have pegged him as a kindergartener, not a three year old. I'm the cynical sort, but I suspect that effect was deliberate; they tried to make him look older for maximum shock value, because controversy sells magazines.