Owned/maintained by the MOD and the terminal/pax side of things is HMGoG as far as I am aware.
All of Jet2's newer 737 800's are fitted with the short field package, which allows GOL to operate in and out of runways considerably shorter than GIB, so landing distance shouldn't be a problem for the 738.
Airlines also operate non-short field 738's into and out of places such as Skiathos every day, on sector lengths of up to 2 hours. They've even been known to operate direct back to the UK, loads permitting.
There will still be 737 300's around for a few more years, and who knows, Jet2 might end up with some MAX's
When you consider "Jet2CityBreaks" is one of the "Jet2/Jet2Holidays" spin offs, the fact that Gibraltar has been seeing huge growth over the last 18 months and has become a more popular place to visit, and the fact that they've lost almost half their traffic - as well as all the potential to serve the Western costas for holidaymakers... I hope Jet2 do pick up ops at GIB, because I think they could become a big player there. They've made a success of Almeria.
I just got back from Estepona yesterday, and I'd have killed for a GIB-NCL flight, rolling in from the bar at 4am to get to AGP