Unfortunately, this game is such a buggy disaster, that you might not even realize the cutscenes aren't working during the campaign. Here is a guide to which cutscenes to watch, when to watch them, and you can watch them here. This way you can just pull up the guide while playing, watch the relevant portion when it matters, and then get back to playing.

I personally wanted an easier way to access them and play only the bit missing for each mission, so this was the result. Each video is limited to the portion you need to watch. So no need to worry about starting and stopping at any specific points.