It's important to note that the interesting scenarios described in the article still boil down to a headline like "Countries are still responsible for the misdeeds of their citizens in the networked world." All the scenarios involving war with China (or other countries named in the article) require hostile acts by persons in China (or the other countries) and an inadequate response by the national government.
What's also notable is the ease and scale that these events can unfold. It's substantially easier for a small terrorist group to exist in (the USA (e.g. Anonymous, by some standards), Russia, China, the Bahamas) and exercise its influence on other countries. There are no need for passports to get there, only an internet connection.
I think there might be a few service-people who would be disgusted at the use of the word 'war' for the App Store or AWS going down.
I don't think the author means it would be war if they went down. More likely, he means that if China attacked Amazon, it's possible that the US would retaliate in a way that escalated into something much worse. Losing the App Store isn't a war. Punishing the perps through increasingly militaristic actions might be though.