How to copy text from the chat window in the Zoom meetings desktop client?

As music2myear already pointed out, the meeting host can disable this function. There is a workaround, but it only works when you are connected via browser: per default the selection and copy of text is disabled in the browser as well if the host has disabled it, but you can use a JavaScript Bookmarklet like this one to allow text selection and copying of said text. Note that this is probably not intended by Zoom so maybe there are any legal issues with this. Nevertheless it works.

It is a specific function of the Zoom client that the Zoom meeting administrator can apply that prevent saving meeting chat, or copying text from the meeting chat.

If the meeting administrator has chosen to prevent you from saving or copying the chat, then you cannot (or, at least, should not).