In reference to the DM's comment, if the will of Gruumsh was taken account of, Karok would just instruct them to attack the dwarves, and if they die, they die. Strength of arms is all that Gruumsh cares about, and Orcs are the only ones he cares about. Especially in regard to Kobalds.
However, the Magic Missiles was mainly due to the insult (calling him weak in front of everyone) and then turning his back on the orc. It was the ultimate challenge. In Orc society, had he simply let the challenge go without a fuss, he would have appeared to be just what the bugbear had called him: weak. Someone who appears weak in Orc society is someone who will soon be dead. He couldn't allow that. By answering the challenge with an attack, even one that doesn't kill or maim, he shows he is not weak, and therefore keeps face.
It was all in character. And I don't think Karok will feel the need to lash out at every challenge. He's proven his point. The others know he's not weak (or at least, he believes they do), and so he is satisfied. He will likely continue to try to assert dominance, but it's possible he could accept someone else's leadership should they prove to be the more effective leader. He will just always be there to...keep them on their toes.