So, is "quality shooting" an official term to describe a bunch of
disciplines (like traditional archery etc.)?
No, de facto, I'd never met such interpretation even unofficially.
Is it really true that we call these kinds of archery "quality
shooting" or did they want to make a joke (mock compound and crossbow
It looks like a strange phrase, yes. What are their reasons to mock customers with undecipherable bad jokes? They also have targets labeled for composite bows. So, the "so called" mockery is an assumption. So, here is my assumption, there is a comma instead of a dot.
This type of target is intended for qualitative
It is not intended for shooting with composite bows and crossbows.
In the video, they're using light bows with training arrows. Perhaps, most of the crossbows shred the target or displace it even with special bolts. Those who have written this, possibly, had a practice with them and just trying to help. Ask them for some clarifications.