That appears to be an odd glitch, photos are working but videos are not. Try restarting your phone if you haven't already and see if that makes any difference. If it didn't go into the Apps menu in Settings, find and open the Camera app listing, tap on 'Force stop', and then find and tap on the Clear cache button. Then start up the Camera app again and see if that made any difference. If that doesn't help, do the same thing again but this time use the Clear data button. Using Clear data wipes the app's configuration and settings files, and its cache so it essentially returns the app to its original first time used state. If you made any alterations to the Camera app previously, you'll need to redo them. Hopefully that step works out.
(I'd suggest trying a third-party camera app too, but the pre-installed, Samsung Camera app is a pretty feature-rich, robust camera that also takes advantage of all the unique hardware features of the camera module itself that independently developed camera apps cannot.)
