Hi AntonLargiader,
The mute switch on the iPhone will not affect video playback volume, however you should be able to change playback volume in one of two ways -
Use the volume buttons on the side of the iPhone or
Tap on the screen during playback and a slider appears on the lower left. You can drag this to change the volume setting.
See this article -
iPhone: No ring or sound from built-in speaker
If this is not functioning correctly, I would suggest starting troubleshooting by quitting all applications on the iPhone and testing. See this article -
iOS: Force an app to close
If this does not resolve the issue, restart the iPhone -
Turn your iOS device off and on (restart) and reset
If the issue is still not resolved, back up the iPhone's data and restore it as a new device -
iOS: How to back up your data and set up your device as a new device
Thanks for using Apple Support Communities.
Best,
Brett L