Sadly, it's exactly as you suspected. (It's only possible to use YubiKey for 2FA). - It's simply not physically possible to set it up so that yubikey "replaces" having to use a username and password completely. So for no password methods of login, the only real way to do that is the "Sign in with Google" button login method. Just keep in mind that the "Sign in with Google" button method of login only works when the email address of your Dropbox account is identical spelling as your Gmail email address. I hope this info clarifies things.
