Regarding Twistor Theory - what exactly is meant by points in space time being elementary objects in physics?

This is part of the dialogue of a video I was watching

"Penrose motivation for twistor theory is to formulate classical physics in a way which uses complex numbers, in doing so he produced the non-local theory of physics, let me explain that, it is the more far reaching departure from a notion of a point or event as an elementary object in physics. What you do in twistor theory you assume that space time points are not elementary. They are derived objects. What instead are fundamental are light rays."

and later on in the video

"Points and events in spacetime correspond to extended objects curves in the twistor space and conversely points in the twistor space correspond to light rays or null surfaces in space time. .... A point is not fundamental"

I kind of understand what they are saying mathematically with respect to points, but how does physics treat points as fundamental? I never really thought about anything in physics in terms of points or curves, just forces, particles, energy etc.