Certainly looks like a dead one, but it's not unusual to see dead red rock crabs (particularly females) around this time of year and into spring- just old ones that run out of gas. The goo is bacteria that grows on anything that is decomposing; you don't see that on molts.
Crabs molt the surface of their gills along with everything else, so seeing gills doesn't mean it has to be a dead one. The eyes on molts are clear, never dark, so that's a good way to distinguish molts from dead crabs. Or you can pick it up and then smell your glove after the dive- if it was dead for very long, you'll know it!