The author never claims that the assassination did not cause the war. Even though the author believes the assassination was only a cause “in a trivial sense”, it still counts as a cause.

The argument doesn’t make any claims about whether the circumstances leading to the war were inevitable; the author does claim that the given circumstances would inevitably lead to war, but maybe something could’ve been done to prevent those circumstances.

This is a fair restatement of the conclusion. The author agrees that the assassination caused the war, but argues that the conditions of the time were a “deeper,” i.e. more fundamental, cause. This is why teaching that the assassination alone caused the war is misleading.

The author doesn’t speculate about what might have happened if the conditions had been different. The argument is simply aimed at clarifying that the assassination was not the most important cause of the war.

The author doesn’t speculate about what might have happened if the assassination hadn’t occurred. The argument is about what can be considered a cause of the war, and to what degree; it’s not about a possible alternative history.