TLDR Gaussian splatting.

What is missing from the article is that creating a model from a few pictures is not that hard (well it is to do well, but hear me out)

The difficult part is animating it realistically with the sensors you have, in real time.

Extracting signal from eye-gaze cameras with a sighlty wider field of view, that allows realistic not not uncanny valley animation is quite hard to do on the general public Peoples faces are all different sizes and shapes, to the point that even getting accraute gaze vectors is hard, let alone smile and check position (those are done with different cameras, not just eye gaze. )

This is what fascinates me as well. I have to assume there's a neural net that effectively learns all of the possible muscles in the face. The limited sensor data gets fed in, and it's able to infer the full face shape. It seems perfectly plausible in theory, but I'm still impressed it seems to work so well in practice.