Take a look at the docs for Catalyst::Component, which says:
The component's config hash is merged with any config entry on the application for this component and passed to new() ...
Which is quite a useful feature! This basically means that you can populate any attribute in the class from the config option.
In which case, you can create a single base class for all your models that derives from Catalyst::Model::REST and set the credentials in the attributes in that class. However, that will not allow you to put credentials into external configuration file.
package MyApp::ModelBase::REST;
use Moose;
extends 'Catalyst::Model::REST';
has '+username' => (default => 'username');
package MyApp::Model::Game;
use Moose;
extends 'MyApp::ModelBase::REST';
The only way I can think of achieving this with external configuration file is unfortunately to duplicate the data, unless you use Perl file as your config, in which case you can define variables and re-use them inside the config.