downloaded and extracted the .210 dll file successfully from https://www.powershellgallery.com/packages/PackageManagement/1.1.7.2
Placed into the working directory per instructions....
NuGet
--2.8.5.210
----Microsoft.PackageManagement.NuGetProvider.dll

Script navigates to the Modules\VMware.PowerCLI-11.0.0-10380590 successfully and that that is when it states it still needs "NuGet provider is required to continue"
"PowerShellGet requires NuGet provider version '2.8.5.201' or newer to interact with NuGet-based repositories..."

I went above and beyond the script by placing the Microsoft.PackageManagement.NuGetProvider.dll
in the c:\Program Files\PackageManagement\ProviderAssemblies\nuget and c:\users%userprofile%\AppData\Local\PackageManagement\ProviderAssemblies\NuGet directories and verified the script placed the .dll into the c:\Program Files (x86)\PackageManagement\ProviderAssemblies\

What is continuing to trigger the NuGet?

I've downloaded and tried different VMware.PowerCLI Modules version from both the PowerShellGallery and from https://code.vmware.com/web/dp/tool/vmware-powercli sites.

I saw the https://blogs.vmware.com/PowerCLI/ mentions under known issuese suggesting getting something newer than the standard "Older versions of PowerShellGet (Example: 1.0.0.1) will fail because it can’t handle the formatting of one specific PowerCLI version."

What version have you tested for PowerShellGet? I'll have to try that tomorrow since I"ve been trying this all day to work :(