I think the issue is that your computer does not support Mojave and although works well in most cases there is some compatibility issue with Zoom.
I have the same computer with a Mojave partition and a High Sierra partition. Zoom works perfectly in High Sierra but in Mojave the camera is functioning and other people can see me but there is no video, just like your problem. FaceTime works fine on both partitions.
It is possible that updated versions of Zoom will fix the issue but I doubt it. If you need Zoom, I would suggest that you either partition your HD and set up a HS partition, or downgrade to HS instead of Mojave.