Please re-read the objectives. You do not talk to the "storm flyer at the airship landing" in order to receive this quest. After you get the quest, the first thing you need to do is talk to the storm flyer. It's an objective that is part of doing this quest.
This quest comes from an NPC called 'Trachraet' at 'Maelstrom Command', which is the Maelstrom Grand Company Headquarters. Please look in the upper right corner of the quest box we have, where it says "Issuing NPC:". That's the NPC that gives this quest to you :)
Here's a picture with a red box showing you the information that's been here for over a year.