I purged the Varnish cache.
And... the issue is still there.
I use the MacBook Pro now to create Layouts with Views included.
So I was able to clean my setup from the unnecessary content templates.
But the mystery is still there.
Same OS, same browser on the client side,
Same WordPress setup and same host and server (of course) on the server side,
=> two different behaviors...
I have found that there is responsive issue on large screens with Inserting View popup.
Please add below code into your theme/functions.php, it will display ”Close this view and return to the Layout” button properly when Inserting View in the Layout at your client's end (iMac 27, Chrome).