I am not sure what's the point is. It's still recursion it just bypasses using frame pointer and simulates its own. Here with set but stack is customary way to do that.

The idea isn't new either. Link to C implementation of quicksort without function calls: http://www.ucw.cz/libucw/#what (simple implementations is in array-simple.h). This implementation is very similar to the one in the article and is way (in my experience often more than 2x) faster than qsort or std::qsort so worth taking a look at.