Emirates couldnt swithch, the runway is not long enough for the 773, plus it carries over 400 pax, the terminal couldnt cope!
Runway length wouldn't be a problem, GLA's runway is only marginally longer than EDI's. As EK said in that report it's the terminal/stand availabilty that would be the biggest issue. However, I don't think it's a realistic scenario, and I don't see EK ever switching ops from GLA to EDI. It's much more likely that they might add an EDI service in the future but that would be aswell as the existing GLA service.
As CabinCrewe says, the A330-200 could be used by Emirates or others to EDI but would need to use 6A and would probably overload the international arrivals and departures facilities.
There's 5 stands that can take aircraft bigger than B763. For an A332 6A, 17, 23 and maybe 18 and 21 (again wingspan could be an issue but they can take up to B764). All would involve knocking out adjacent stands either side though, and all would involve bussing inbound pax to immigration.