The comment you replied to is surprised that they did use their own TLD, thinking they should stick with their classic domain on not their own TLD (google.com)
However, using their own .google TLD makes sense the closer I looked at this link after you brought my attention to it.
This appears to be a branded and hosted version of a third party learning platform that might be simpler to deliver a whitelabeled expereince.
The login experience (either to use your google credentials or create your own account) seems to be the confusing piece.
I would not be surprised if this is not a third party piece of software in which case the login screen makes sense.