A Torumekian airship in distress appears over the Valley of the Wind. Despite Nausicaa's efforts, it crashes with the loss of all hands. Soon after this, the peace of the valley is shattered when Torumekian soldiers invade. They almost immediately take control, as the Valley people are unprepared and militarily overwhelmed. Torumekians, in Medieval-looking armour but carrying automatic weapons, enter the castle of Nausicaa's father King Jhill. A few shots are heard, then we see King Jhill on the floor dead. Although he draws a sword we already know that he is bedridden and not capable of resisting physically, the Torumekians seem to have simply opened fire without warning or explanation.
Their actions don't seem to make sense once we understand the motivations of Princess Kushana, commander of the Torumekian forces. The crashed airship contained an embryonic God Warrior, a weapon which she believes can be used to destroy the giant insects who are now the dominant life form on Earth and threaten human survival.
Later, Princess Kushana gives a speech inviting the Valley people to join them in this enterprize and promises them a life free from fear if they do. So, why kill their king?
It could be simply a gratuitous action to establish the Torumekians as the bad guys, but this doesn't seem to be director Hayao Miyazaki's style. Kushana is no one-dimensional villain: she's ruthless but her motives are relatively humanitarian (as compared to others who Kushana knows will seize the God Warrior to use as a weapon: this appears to be her main reason for occupying the Valley). King Jhill was not capable of leading any resistance. If he had been left alive he could have ordered the Valley people to co-operate with the Tolmekians.
Ironically, once people find out what has happened to their king people want to fight twice (first Nausicaa, then the entire valley) and cooler heads have to persuade them that this is suicidal and the only option is to co-operate. This costs Kushana lives (after Nausicaa's uncharacteristic one-woman killing spree). The third time the valley people rise up there is no cool head to stop them and they come close to seizing control from the Torumekians.
King Jhill himself could have been persuaded that co-operating with the Torumekians was the only sensible option at that point, and would have had the authority to order his people to do so. Kushana could have forced him to do this at gunpoint if necessary. So why did her soldiers kill King Jhill?