What's the term for the opposite drawing style to hyperrealism?
These are simply portrait sketches. There's not, to the best of my knowledge, a specific term for the technique other than "sketching".

Sketching doesn't just mean an unfinished work, a doodle, or lack of detail. I think this phrasing from Painting.About.Com defines it well:


  A sketch is painting or drawing capturing the essence of an object or scene, giving an idea or outline of it or simply a part thereof. How quickly or slowly a sketch is completed depends on the individual artist. Some work very quickly and roughly, others slowly and in great detail.


So, in these portraits, capture the eyes and certain features is just part of getting that essence of the person. Eyes are a very defining facial feature, and they're very humanizing and expressive. Adding detail to them is an easy way to make the drawing "pop".

The three examples you've given are distinctly different personal styles. As you seen in the top, it's more defined by outlines, hatching and cross-hatching.  The second works more with fluid lines and varying tones. The last one is kept very loose, using "scribbles" and high-energy lines that go outside of the bounds for the hair, contrasted with well-defined edges and hatching for the face. 

I wouldn't really consider any of these the opposite of hyperrealism, either. You can go much further away from that, such as gesture drawing and cartooning. 

If there is a specific term for this, I've never heard anyone use it. This is the type of art I'm most interested in, so I've seen a lot of it and followed artists for years with no mention. I've also not heard anything used in any art class or tutorial I've taken.

At most, I think you'll be able to break down some individual techniques or concepts, somewhat like I did a couple paragraphs ago. If you're particularly focused on the beauty aspect of them, you may think of them as fashion, beauty or glamour portraits. 

(As a side note, the first one you've listed is actually the most detailed of the three, which is especially obvious if you look at the lips, but there's many more details than that.)