Xbox owners have begun reporting issues launching and purchasing digital games from the Xbox library. Microsoft has take notice of the issue and are looking into it. However, it should be noted that the Xbox Live Service Status page does not report the issues that Microsoft is investigating.
The official Xbox Support twitter noted that they would offer an update on the issue when they know more.
Hi everyone! We're aware some users are unable to launch or purchase digital games. Our teams are on it & we'll update once we know more.
— Xbox Support (1-5) (@XboxSupport) June 4, 2016
How many users are being affected by this service issue is unknown. Hopefully a fix comes soon.