Installing The Zoom Client Without An Administrator Login
Download the latest Zoom client here:
Next, after it downloads, open the Zoom.pkg file:

Click the 'Change Install Location...' button.

Select the 'Install for me only' option.

The software will be installed in your User home folder, under Applications.
FAQ:
Q: How do I know if I have the most updated version?
A: When you're in the Zoom app, under the zoom.us menu (next to the Apple) there is a 'Check for Updates' option. Select that and it will tell you if an update is available.