The install is a two step process. The first step is to unpack the .exe (zip) archive you downloaded from MyEsri to a folder you have write access to. The second step is to run the setup.exe from the unzipped folder. The second step will prompt you for elevated access.
When the exe launches and asks where to store data, don't unpack to C:\Program Files(x86), much better to unpack to another location (C:\ArcGIS, C:\installs\ArcGIS) and after it is unpacked, run the setup (it will then prompt you for the final install step).
This exact sentence needs to be added to the "Install ArcGIS Pro" help page. I had the same issue as the OP because that page instructs users that "The default installation location for a per-machine installation is <System Drive>\Program Files\ArcGIS\Pro." It's correct, but misleading, because the first step as you point out is to unpack elsewhere, then install to the Program Files folder.
They were not unpacking correctly elsewhere either. Windows 10 appears to have been protecting my computer from new threats by making it impossible for me to install them. Turned off that setting, and now we are golden. Thank you!
