Use a column name to specify a predefined table

This is a poor way to maintain referential integrity. There are a number of ways you could approach this.

The first would be to have an address table, then multiple tables to contain the links, e.g.

CREATE TABLE StudioAddress
(       StudioID INT NOT NULL,
        AddressID INT NOT NULL,
    CONSTRAINT PK_StudioAddress__StudioID_AddressID PRIMARY KEY (StudioID, AddressID),
    CONSTRAINT FK_StudioAddress__StudioID FOREIGN KEY (StudioID) REFERENCES Studio (StudioID),
    CONSTRAINT FK_StudioAddress__AddressID FOREIGN KEY (AddressID) REFERENCES Address (AddressID)
);

This maintains your referenctial integrity without needing triggers, and still caters for a 1 to many relationship.

Another option would be to have 3 nullable columns in your address table (StudioID, PersonID, DirectorID), each with a foreign key to the relevant table, you can the add a check constraint to ensure only one of the 3 fields is populated (if this is required).

I much prefer the first option though, it is much cleaner, and also allows for the same address to be used for multiple things.

ADENDUM

If this has to be done using triggers, then I think you would need to use something like this:

IF EXISTS(  SELECT  1
            FROM    inserted i
            WHERE   NOT EXISTS
                    (   SELECT  1
                        FROM    People p
                        WHERE   p.PersonID = i.ReferenceID
                        AND     i.TableName = 'People'
                        UNION ALL
                        SELECT  1
                        FROM    Studios s
                        WHERE   s.StudioID = i.ReferenceID
                        AND     i.TableName = 'Studios'
                        UNION ALL
                        SELECT  1
                        FROM    Directors d
                        WHERE   d.DirectorID = i.ReferenceID
                        AND     i.TableName = 'Directors'
                    )
        )
        BEGIN
            ROLLBACK TRANSACTION;
            RAISERROR('Referential integrity error', 16, 1);
        END

This essentially checks that for all inserted/updated rows a record exists with the relevant ID in the relevant table.

I still stand by my earlier answer though, that this is a terrible approach, and I would question any syllabus this is on!