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 retaliat

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.