For some years Google Chrome has allowed you to add desktop icon for any web page by going to Tools / Add to desktop. Unfortunately this doesn't work reliably on Ubuntu MATE with recent Chromes: The icons could not be moved away from the desktop, or they would open the application as a new tab (instead of as a new window).

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I found it to be easier to add a custom application launcher to the MATE panel.

In the Command field, enter this:

google-chrome --app="https://www.google.com/calendar"

This will open Google Calendar in a new browser window without decorations (no location bar or bookmark).

You will no longer get the website's favicon as a shortcut icon, but there are many great icons here:

/usr/share/Icons/$YOUR_DESKTOP_THEME$/128/actions