The blog post shows an anchor in which some kind of hitch is tied around a tree, and a single strand of webbing leads away from the tree horizontally to, presumably, the top of the climb, which is out of frame.
The blogger seems to be criticizing this setup because there is only a single strand. I suppose this is somewhat valid because if you load this anchor, all of the load is taken by a single strand of webbing. If they instead tied a big, long loop of webbing around the tree, then each strand would only take half the load. But this aspect of this anchor actually doesn't seem like a huge problem to me, since it's being used as top-rope anchor, and doesn't need to catch a dynamic fall. You can't break a piece of nylon webbing with a top-rope fall, unless there's something else going on (e.g., the webbing was damaged by rubbing against a sharp edge).
Assuming that the knot is a good knot, it's dressed nicely, and there are long tails, I would not have a problem trusting my life to this anchor. The tree looks gigantic, and it looks like its roots are solid. (I can't see in the picture whether the tree is alive.) It's true that the anchor is not redundant. However, redundancy is just a rule of thumb -- people often use a single non-redundant anchor when it's as huge and obviously bomber as this seems to be based on the photo. If I had a way to back it up, I certainly would, but using it as is is not stupid, IMO.
Note that tying a big long loop of webbing would not make this anchor redundant in terms of failure of the webbing, because if either strand broke, the loop would come apart.
Most likely the reason they used a single strand is simply that they didn't have enough webbing to reach with two strands.