Since we need to use the google authenticator to login on WEX platforms, I would like to know if the following extension is approved for us to install in the browser instead of having the app in the phone.
https://chrome.google.com/webstore/detail/authenticator/bhghoamapcdpbohphigoooaddinpkbai
Although I'm not sure whose approval you're trying to seek, IMHO, installing an authenticator on your browser is not a very good security practice. The whole point of having a Two-factor authentication system (or a Multi-factor authentication system) is to enhance security and make it difficult for anyone attempting to intrude into your secure logins. Having your Google authenticator in the browser (essentially in the same machine {desktop/laptop/tablet} as you usually login to) defeats that very purpose.
To put it more simply, enabling Two-factor authentication system using Google authenticator on your mobile phone would need an intruder access to both your machine and mobile to login whereas if you were to install the browser extension, the intruder can attempt to sneak in with access only to the machine.