Instantiate a class type from inside a variable?

You can not drag script assets onto variables. Well you can because the Unity editor uses a special class in editor code called MonoScript which is actually a TextAsset. That's what you have assigned to your "Object" variable. You have not assigned an instance of the class which may be defined inside that script file, but the script file itself.

Note that the MonoScript class is an editor only class. So you can not serialize a reference to a MonoScript inside a runtime class. The GetClass method of the MonoScript class actually returns the System.Type object of the class that may be implemented inside that script file. Though, again, this class can only used in editor code. See my answer over here for how to implement a property drawer that allows you to drag script assets onto the field and just have the type name stored.