In real life, with gusty winds, on auto-pilot, does then the engine throttle also move like it does in IF?
Not 100% sure but the yoke doesn’t move so the throttles shouldn’t move aswell.
The engine throttle will move just not as fast as the one we have in IF.
Incorrect. The Yoke and Throttles will move. On Airbus, neither of them move.
The throttles would definitely be very active in a Boeing during gusty winds if the auto throttle was engaged.
I don’t think it physically moves on airbus planes.
No it doesn’t on an airbus.
Is this due to the Airbus fly by wire system?
Depends on the plane, some do, some don’t
Not really, it’s just how it’s designed.