Does Google's PageRank count as a sorting algorithm?
The answer depends on what you mean by a sorting algorithm. The usual meaning is:


  A sorting algorithm is an algorithm that gets a list $L$ of comparable objects, and sorts them in (say) nondecreasing order. The algorithm could only work for a certain class of objects.


If you use this definition, then PageRank isn't a sorting algorithm. But it's up to you.