There is a problem with the new user registration when doing it this way:
Select "Sign In" -> Select "New User? Register here."
This brings up a Register dialog that has no place for a user name and thus one can not register from this dialog (it just says fix the highlighted errors of which there are none).
The behavior is really strange. However, it looks like you have managed to overcome it to create an account, right?
Both listed methods works for me. Perhaps, that was a temporary issue. I think it's resolved for now.
I had the same problem trying to register today, Chrome Version 64.0.3282.167 (Official Build) (64-bit) and Windows 10. Thanks for explaining the workaround