Perhaps the nature of the original sentence's badness would be clearer if we swapped out the praise of authors for the leaves of trees:
The leaves that the gingko has are alone among the leaves possessed by any tree in the whole of the forest.
As username901345 says, the problem areas here are "alone" (when expressed in the context of leaves among other leaves) and "any tree" (when intended to convey the idea of all other trees in the comparison). What you'd want to say is something like this:
The leaves that the gingko has are unique among the leaves possessed by the trees in the forest.
The ginkgo's leaves are unlike any other leaves in the forest.
Similarly, in the discussion of the praise that Twain has received, we would do better to clear out the "alone" and the "any writer" in favor of something like this:
The praise that Mark Twain received differs from the praise given to other great American writers.
The awkwardness of the original wording proceeds from the infelicitous "praise alone among praise" and the unhelpful identification of a single "any writer" to serve for "all other writers."