Latest information - April 9, 2020
Zoom has changed its install/update on macOS. Previously, they were running scripts before asking permission or starting the install.
That made it easier for non-admin users; if the user didn’t have write access to the shared /Applications folder, Zoom.us would just drop itself in the user’s ~/Applications folder where it had full permission to run and update. But after alerts of improper use of Apple’s Installer, the Zoom updates behave in the standard way, which means it will fail for a non-admin user unless they click the "Change install location" button and select "Install for me only" instead of "Install for all users on this computer".
Going forward, you should be able to install the updates this way:
The Zoom installer usually makes it easier for non-admin users to install by automatically displaying the "Select a Destination" window. Users should change the destination to "Install for me only":
But the install script might skip over the "Destination Select" step; clicking Install will prompt for an Admin account:
If "Destination Select" doesn't display on its own, users should click the "Change Install Location..." button to access to the "Select a Destination" screen and select "Install for me only":
This will allow the update to install without having to provide Administrator credentials to allow it.
Direct installer download links: