They can, of course they can. But those rules are for the LAND not the air. Drayton Manor can set whatever rules they want on the land they own. But not for the airspace above the park, which they do not own. When you buy a piece of land, a building, a house, whatever. You never get the airspace rights above your purchase. Ever.
There are many YouTube channels proving this in action. Try DJ Audits. That specific channel even goes as far as flying drones above police stations and after some altercations, gets left alone once the police actually look at and understand the law surrounding drones. Leaving him free to carry on flying over the police station.
The only thing that sign prevents you from doing is taking the drone off, landing the drone and controlling the drone from the land owned by Drayton Manor. You are free to do all that from an adjacent piece of land.