These mics are $3000 each, and the solo parts sound fine, so I assume they're working. However there are very directional capsules available for them, and it'd make sense to use those on a stage that's built to reflect unplugged sound. Unless you're dancing all the time and can't hold the thing close enough and centered to your mouth...
Another explanation is that the girls never really sing the group parts, to save breath, but they disabled the playback because they're so close the audience would notice.
I think usually Momoclo use backtrack for reffs or parts when they sing together. But in this case, the music seems not loud enough, so did the backtrack. You can hear that the girls sing much louder than the music. Probably only happen on TV but not for live audiences.
Since this was broadcast in 3D it probably had surround sound as well. Maybe whoever uploaded it just stripped the rear channels instead of mixing it down. Anybody got the transport stream to confirm?