It was removed/disabled a few weeks ago due to a bug. Based on the email sent out to developers using the feature it sounds like it may not be returning:
There is an issue with a feature you have used within an extension: Request Broadcaster Permissions. This issue prevents Extensions from properly using this feature and blocks broadcasters from activating Extensions. Due to limited use of this feature, coupled with the fact that an extension can provide the same functionality within a configuration page, we have decided to disable this feature until further notice.