Amazon is an extremely visible American company, hitting their assets carries a symbolic meaning even if the DoD wouldn't have anything running on that datacentre at all. Iran's trying to transmit a message of "we can destroy your stuff too", trying to impact the general US feeling of invulnerability.
I don't think it'll work, but they might as well try I guess.
> trying to impact the general US feeling of invulnerability
Or, perhaps, trying to defend themselves? They are being attacked, after all.
Not just Amazon - I guess the Oil and gas industry is now run on the cloud. They used to have big SGI machines 30 years ago... but I bet everything is on the cloud now using GPUs.
> I don't think it'll work, but they might as well try I guess.
Consider this from the eyes of the people living there. Your world is peaceful one day and burning tomorrow. It doesn't have to be "burning like hell", but something came from the sky, entered your building, exploded and damaged some stuff to the extent that fire-supression triggered and damaged more things.
Even if it's not a trauma, it's a shock. Something you'll be remembering for a long time. We live in fragile bubbles, but don't know it until we experience it pop. While this might not make them "win" the war, it'll leave a mark and make the affected persons' ears perch up to understand what's happening better.
Please note, I'm not from either side. I'm a close observer because of where I live, and still believe that this should have not happened.