When the Geeks use "Control Minion" on a played minion (a Shoggoth in the case in question), who gets the benefit of making other players draw Madness or destroy a minion?
The controller steals the effect.
As long as you play Control Minion according to its special, the controller uses the minion's entry effect. Otherwise, the card would say "Special: Play after another player plays a minion."
The game uses "after" a minion is played to clarify that its entry effects occur first (such as with the Leprechaun). That wording isn't used here.