You can try to reset his iPad to get this solved. This won't remove data or settings, it could help you get rid of the bug you're experiencing. To reset, press and hold Home and power button at the same time until the Apple logo appears. Let go of both. The iPad will power up on it's own.
Force closing the app might help as well:
Double tap the Home button to show the multitask bar. Then slide the picture above the app icon towards thentop of the screen.
If the steps above don't solve your problem, you'll need to provide more information:
What does he use to watch the videos: a browser, the Youtube app, or a similar app where he should be able to watch them?
Is he logged in/does he have a Gmail account?
Is the iPad up to date? The most recent software version for the iPad mini is 8.1.3.
What exactly is happening when he tries to watch a video?