Why did the gamemakers shoot fireballs at Katniss and was it cheating? I thought that the fight was between the players not the organizers.
The books explain it. It's not cheating, it's a way to ensure the games are interesting for the viewers. When a tribute is too far away from the "action" the game controllers force them back towards the others.
The Gamemakers use fireballs to force the tributes closer together in the arena. During the 74th Hunger Games, the Gamemakers injured Katniss's leg with a fireball. The Gamemakers planned to use the fireballs to decrease the distance between Katniss and the Career Pack, or kill her if necessary.
Katniss had gone too far away from the rest of the tributes and isolated herself, and so the gamemakers wanted to bring her closer to the others.
It was not cheating, in my opinion, because their intent was not to kill her but to bring her within the proximity of the other tributes. Katniss herself was cheating, in a way, by isolating herself and possibly attempting to win the games without having to kill anyone or be in a situation where she may be killed.
The game makers saw katniss heading to the end of the area, so they set up a forest fire to drive her away, and toward the career pack so that they could see so 'action.' When katniss started to run away from the fire the game maker put fireball to make it more fun to the audience, which burns katniss leg and into the career pack.
Imagine in a video game match where players are in direct combat, one player moves as far away as possible from the action in order to survive. Gamemakers (both real and fictional) prefer that players adopt the more aggressive style of play, and so they send the message to "Return to Battlefield" and punish those who fail to do so with death. This is essentially the same thing that the Gamemakers of the Hunger Games do.