How do I download/extract font from chrome developers tools?

Right-click, then "Open link in new tab"

edit : you can also double-click, it has the same effect

To get .woff fonts first open the chrome dev tools panel (Ctrl+Shift+i) go to Network and reload the page. There you will see everything the page downloads. Find the .woff file, right click and select Copy response.

The response will be a url so paste it in the navigation bar. A file will be downloaded, just add the .woff extension to it and voila.