I think that the ATC controller sounded more nervous than the pilot. Endurance and/or fuel on board may become important if the weather is so poor that the flight need to be redirected or saved and ATC need a clue what alternates make sense. However direct after take of at the same airport souls on board should do, so the firecrew has an idea on how may to rescue in the worst case. The pilot asked for altimeter, wind and weather which is the most important for his pattern planning. Good comms from the pilot and a happy ending. On a Mayday aircraft with engine on fire ATC knows that the pilots are busy with checklists and trouble shooting. So questions from ATC should be kept to a minimum. Too much RT can result in distraction and shutting down the wrong engine. We had examples where that ended in pilots swim operations on a twin.