Don't be embarrassed - it's a good question!!
I've never been 'trapped' and know little about carrier ops. Perhaps the SOP with a fire on deck is that the pilot has to shut everything off, make the seat safe and then egress. The fire seems to have been brought under control pretty swiftly and it's likely the pilot was in comms with FLYCO. Just leaving with the engines running and loads of fuel still pumping poses serious risks for the entire ship and its crew (remember Oriskany about 1967 {and there was another one too}).
There'll be some very experienced naval aviator along with the real story soon!
Old Duffer