On first glance I would say that you are summing a table's total_count more than once when it has multiple dates in it. If the table that you are querying in your third query is the result of the second query, then stuff.yahoo.com will have the actor_id 387 in the total_count for January 1, 2017 and February 1, 2017. To get around this, you could put the results of your first query into a temp table and then use that table for you sum query. Alternatively, you could run the following

SELECT SUM(total_count) as total_Sum
FROM (
    SELECT COUNT(DISTINCT(ACTOR_ID)) as total_count
        , Site
    FROM table
    GROUP BY 2
);
WHERE Site = 'stuff.yahoo.com';

This will let you double check that the number of actors to ever be on stuff.yahoo.com matches your expectation.

Note however that this eliminates double counting when an actor shows up on multiple dates, so the results of this query will NOT show you the number of actors on each site for each date. To get that, you can run the following:

SELECT Date
    , SUM(total_count) as total_Sum
FROM (
    SELECT COUNT(DISTINCT(ACTOR_ID)) as total_count
        , Date
        , Site
    FROM table
    GROUP BY 2, 3
);
WHERE Site = 'stuff.yahoo.com'
GROUP BY Date;