Hi RoffleCopter,
You can register your domain name with a domain registrar of your choice and signup a hosting plan with other web hosting provider, both of them need not to be from the same company.
A little extra on your video game site, perhaps you can consider building it with open source program like joomla, mambo, drupal, phpnuke, many communities are using these open source cms as the community platform, and these open source programs are mostly php / mysql based, which is supported in most linux based web hosting plan.
Hope that helps
