Ok, it seems there is a misunderstanding somewhere :P What exactly do you do on your wiki to login? You simply need to click the "Login with Google" button, no need to enter the e-mail address or even the password of your Google account in the login form.
About the two-factor-part: You do not need to do anything to support this. The extension does not need to support or even do anything special for anything login-related stuff on Google's side. If you click the Login with Google Button, GoogleLogin simply delegates the login process to Google (where you have to do anything you need to authenticate). After your login was successful (no matter how many steps and things you needed to do), Google will return the required data back to GoogleLogin. This is the only thing, GoogleLogin needs to know about, anything else is a black box from point of view of GoogleLogin.
Long written things short: Two-Factory auth _on Googles side_ is perfectly well supported by GoogleLogin.