The lines between IaaS, PaaS, and SaaS aren't always hard and fast, and it isn't just about software installation but also software management. For example, when you spin up a Windows Server VM on Amazon EC2, the VM image you spin up was built by Amazon (it is common to use Amazon's images instead of building one's own) but the customer is responsible for managing it, updating it, etc... One could argue Amazon installed the OS, but nearly everyone still considers AWS EC2 as IaaS.
I am not sure if your question is about cloud services in general or ArcGIS Enterprise for AWS. In the context of ArcGIS Enterprise for AWS, it might be Esri's tools that are installing the software but it is still the client/customer installing the software on IaaS, they are just using tools by Esri to simplify the process.