It's stage makeup. Made to be visible to the on-site audience.
How does that make a difference? And it’s more than just making features visible, I have noticed heavy red lipstick, dark eyeshadow and even false eyelashes on 13 and 14 year olds.
I don't often get to watch the juniors, so I can't comment on the suitability of Eteri's skaters' makeup. But the basic principle of stage makeup is that the makeup has to exaggerate the features so that they can be seen from far away, which in turn allows changes of expression to be seen from far away. It's hard to see someone's face even from the back half of the stalls/orchestra of a theatre, let alone the top balcony. To help people beyond the first few rows appreciate all the subtle facial expressions that go into a great performance, and to keep performers from having to overact to project their performances beyond those first few rows, performers and makeup artists use precisely those tricks you mentioned: dark eyeshadow, heavy eyeliner, false eyelashes (to make the eyes and their movements--a subtle narrowing or widening of the eyes, for example--visible); dark lipstick (easier to see from far away than lighter shades, and essential for reading facial expressions); and sometimes heavier blush or contouring of the cheekbones than you would see in street makeup. You'll see the same thing if you look at images of dancers made up for performance.
But the trade-off, of course, is that the same makeup that's essential in the theatre or arena looks overdone in close-up. Filmed performances of stage plays often have a similar problem; you can see the makeup much more clearly than the live audience can, and the obvious artifice can be distracting. Performers have to choose the audience they're making up for. For actors and dancers, the primary audience is obviously the people in the theatre with them. I assume the same reasoning applies to skaters: not only does an engaged live audience support and encourage them as they perform, but that engagement can influence the judges' perceptions of their performance. Looking overly made-up to a television audience may be a reasonable price to pay for that boost.