2 factor doesn't protect against phishing. It's trivial for a phishing site to ask for a 2fa code, and then immediately use that to sign in on your behalf.
Of course, the fact that he's asked for a password while being already logged in on Gmail is also suspicious, but less so since other sites do that.
While I haven't see it reported whether or not they had 2fa enabled, we can hope that they had taken this very basic security measure.
Actually one of the best preventions against this is using a password manager. I was nearly caught by a phishing site once, and I only noticed because 1Password was refusing to autofill the password field.