That is a very old paper, corresponding to version one of the software. It is now on version 4.x. It is best to see the current documentation for how to use the Bloch sphere: http://qutip.org/docs/latest/guide/guide-bloch.html
This doesn't really answer the question as it's not an online simulator. It might still be relevant though as it is a way to produce this sort of gifs if one has access to the software.
It is relatively easy to do this sort of things using Wolfram Mathematica.
As a quick and dirty example, if we just define a couple of relevant helper functions:
pauliX = ...
I used this last time I needed to look up something about Bloch sphere. It's not perfect, since it doesn't allow entering the exact values of angles, let alone 2x2 matrices, but it has the benefit of being available online.
This one looks promising in that it allows to enter matrices (and is also online), but I haven't tried it.