This question is asking about the final moments of the story. Eckels, Travis, and the rest of the safari group have returned to the present. Unfortunately, it is not the present that they left earlier that day. In the past, Eckels stepped on a butterfly which caused cataclysmic changes to occur in the timeline. Eckels is completely blown away that such a small change in the past could have such huge consequences. He begs for the possibility of going back in time and correcting the mistake. That possibility is not even entertained, and Travis shoots and kills Eckels.
Eckels moaned. He dropped to his knees. He scrabbled at the golden butterfly with shaking fingers. "Can't we," he pleaded to the world, to himself, to the officials, to the Machine, "can't we take it back, can't we make it alive again? Can't we start over? Can't we-"
He did not move. Eyes shut, he waited, shivering. He heard Travis breathe loud in the room; he heard Travis shift his rifle, click the safety catch, and raise the weapon.
There was a sound of thunder.
Whether or not it is fair that Eckels dies is entirely up to individual reader opinion. You can safely state your opinion, but remember to explain why you think what you think.
Personally, I don't think it's fair or justified that Eckels dies. I believe that Travis shoots Eckels more out of anger and revenge than punishment. Nothing can be done about the changes that happened, so I don't feel that Travis shooting Eckels is a punishment. If it were a punishment, it's a useless punishment. It doesn't solve the problem in any way. Killing Eckels doesn't help the situation. Leaving Eckels alive won't cause any additional harm, either; therefore, I don't believe it is fair that Eckels dies.