Anyone know what particular species they fish for at that depth?
Whale turds. That's the bottom of the ocean.
Seriously though, there is a deep water fishery in several parts of the world. That's where orange roughy comes from (well, used to come from, until they wiped it out).
Populations of north-east Atlantic commercial deep-water fish such as black scabbardfish, orange roughy and roundnose grenadier have dwindled since deep-water fishing started in the area in the late 1980s but a quota system wasn’t introduced until 2003... The story and a very good site...Deep sea fish suffer far greater damage than was first thought at The End of the Line Blog