It was a gem compatibility issue.
After version 1.1.4, the structure of devise_invitable changed.
devise_invitable/controllers/registrations
no longer exists. Therefore
module DeviseInvitable::Controllers::Registrations
needed to change to
module DeviseInvitable::RegistrationsControllers
to reflect the structure of the updated gem.
The other solution would be to add the version number to the gemfile and make sure I am using a compatible version so that things are being referenced as expected.
The server and rake commands now run, but there are a number of other issues I have to figure out now :P