It is truly interesting the way the distances can be estimated and compared to the speed of light.
However, there is something my non-mathematical brain (as RL would say) does not understand.

The article states that the distance to the gamma-ray burst is about 13 billion light years away from us, and the event happened about one billion years after the big bang.

Now lets imagine ourselves at the moment of the big bang, we are at the beginning, with the star that will create the GRB, now the BANG happens, lets say the star now is moving away from us and we are moving away from the point of the big bang, we wait for a billion years and then the GRB will occur; now, the question is: How fast do we need to be moving, so that the energy of the GRB will be delayed for 13 billion years before we detect it?

Johannes