Joerg: Extraordinary help - you nailed it. Thank you for taking time from your day to make mine so much better.
Just for future reference, the zip archive that finally worked was a zip archive nested inside of the zip archive that is provided as a download.
The download was VMW-ESX-6.5.0-arcmsrn-2.00.00.05-16913232.zip
The folder nested inside was VMW-ESX-6.5.0-arcmsrn-2.00.00.05-offline_bundle-16913232.zip
Used WinSCP to copy that nested zip archive (left as a zip file) to the tmp folder of the ESXi installation, then used Putty to SSH the following command:
esxcli software vib install -d /tmp/VMW-ESX-6.5.0-arcmsrn-2.00.00.05-offline_bundle-16913232.zip