If you don't have a default email address configured on your computer, when you click on an email address you won't be redirected to your Gmail mailbox, an error message will appear where nothing will happen.
To get Gmail to open when you click on an address like in the picture below, follow the steps below.
Step 1 (Windows): Set Chrome as your default web browser
In the Windows search bar at the bottom of your screen, look for the settings window: "Default applications".
Set "Google Chrome" as the default application for opening Email
Step 2: Set Gmail to Chrome
Open your Gmail inbox from Google Chrome
Use the following hotkey combo:
Ctrl+Shift+J (Windows)
Cmd + Opt + J (Mac)
This will open the JavaScript console for you.
Then enter the following commands and validate:
navigator.registerProtocolHandler("mailto",
"https://mail.google.com/mail/?extsrc=mailto&url=%s",
"Gmail");
A popup window will appear at the top left with the text " mail.google.com wants: Open "email" links" and offers you the possibility to authorize or deny this access, in our case we are willing obviously allow it.
Now when you click on an email address you will be automatically redirected to a new message in Gmail.
Important: If however, this does not work, go to the following page: chrome://settings/handlers
Remove mail.google.com from the list of unauthorized protocols, then repeat the previous steps.