Is there a gesture-like exercise for drawing faces?
Many people told me doing gestures is great as a learning tool, gives you the pencil mileage, feeling for shape, form and proportion, and so on.
I've actually found doing gesture drawings fun and helpful - I'm seeing improvement! I began wondering - are there any similar, established exercises for drawing faces?
The links you provide are are illustrating exaggeration, not gesture drawing per se.
Gesture drawing "proper" is an attempt to get at the essence of a pose without falling to nitpicking details. It is a good exercise only insomuch as it trains you to develop a context and a framework for the further detail you will inevitably bring later on.
The problem with gesture drawing and especially the videos you link is that they are impressive to you as a learner, but exaggerating features immediately distorts the entire scene which you are mapping. When you go deeper and develop the drawing, all of the established relationships within the drawing will be inaccurate and you have no firm framework for measurement.
For artistic synthesis, this isn't a big problem, but your question itself implies that you are interested in accurate rendering.
If you apply the techniques displayed in those videos to faces, the thing most people are most familiar with, you will never get beyond caricature.
Zen Observation of the Day: in a drawing the difference between a finger pointing and the middle finger is about 1 mm and 4 degrees rotation.