According to MacStories, the app works by simulating an AirPlay mirroring connection to the app itself. Capturing begins when a user toggles "Device Screen" within the app, exits the app and then chooses Vidyo! as an AirPlay source in Control Center.
While the app is currently in the App Store, it's unclear whether Apple will pull the app as it simulates AirPlay mirroring. Apple doesn't currently provide APIs for iOS devices to act as AirPlay receivers and, according to App Store Review Guideline 2.5, apps can be rejected for using non-public APIs.
Vidyo! is available in the App Store for $4.99. [Direct Link]
Update 1/7 9:30 a.m.: Vidyo has been removed from the App Store and is no longer available for download.