AWS is just a platform to host the backend application. The same backend could be hosted on any cloud or on-premise servers. The frontend is the app itself, settings, users and content are stored in a database. So if they have copies of the database, it's just a matter of getting that database restored, some front end servers and load balancers as well as changing some IP/network information for DNS. They'd be 80% or more backup and running.
I’m a CRM consultant so I have a working knowledge of app architecture - good explanation & makes sense