Hi
Ouch, he does sound in a bad way.
I personally would acclimate him and put him in the tank (as long as there are no other fish in there already), on the grounds that lots of clean fresh water is often the best cure for fish ailments. It is possible that his cup water is simply full of ammonia/nitrites or the pH in it has plunged, causing th gasping and slime coat sloughing.
I would also add 1 level teaspoon of salt per gallon to the tank (any salt unless it has anti-caking agents in it, completely dissolved first in some tank water and poured into the tank well away from the filter or fish). A mild salt solution usually helps sick fish. Keep the tank light off and don't feed him for a couple of days.
Hope this helps, and good luck.