fairly clever use of a combination of techniques ... my guess
1) AI face feature recognition to identify mouth, nose, contour, eyes, tec
2) assignment of spline control points based on features, perhaps based on some generic facial profiles
3) 2.5D distortion (rotations, shears, projectioons)
4) bump texture mapping with some tunings based on feature and adjusting for obscuration
5) rendering into a animation with matching speech (see crazy talk)
All fairly mature tech (except #4), but an interesting combo which relies on a decent cloud rendering pipeline
Note that with some really advanced refinements, you can then snub-dub your own movies, adding in frienemies (within reason) for similar actor(ress) substitution.
double plus good!!!
Lawrence