I think there has been some serious misinterpretation of what 'real time' means in the context of this paper; and, possibly, that the researchers have avoided overt clickbait claims because they knew the term 'real time' would do the work for them.

This is not some neural codec that can convert any novel or unseen object live, like a kind of 3D YOLO - the paper mentions that it requires up to 24 hours of training on a per case basis.

Nothing can be edited, no textures or movements - all you can do is remove people or speed them up or slow them down, and that's been possible in NeRF for a few years now.