Hi,
I will have to make a couple of assumptions in order to attempt to answer your question.
I am assuming that what you want is a common implementation for the two actors and not an interface that allows you to implement different logic for the two actors.
For this purpose you should implement a common class e.g. GhostBase which inherits from actor and inherit you Red and Pink Ghosts from this common class. There are many other options for doing this but I think this will be the easiest one.
Your specific problem is that an interface does not have access to the world, which is why you are getting the compiler error.
In the second code line you are giving I am assuming that this is either the ghost or the interface which are unrelated to the game mode. The Unreal Cast template is a soft cast and will return nullptr when unable to cast.
I hope this helps you.