From the rulebook:
"CONSTANT ABILITIES If a card has an ability that does not have a boldfaced precursor, the ability is a constant ability that is active so long as the card remains in play and meets all conditions specified by the ability"
Restringuntus's "Play:" ability is bold-faced. Unlike, for example, Mother which simply says "During your draw cards step, refill your hand to 1 additional card." This ability clearly transfers to the new controller if control is transferred; It does not have a bold-faced precursor. Restringuntus's Play ability has a bold-faced precursor!
EVERY other Creature's Play ability would not change the game state at all if control were to be switched to opponent. See Bumpsy, Earthshaker, Ganager Chieftan, Hebe The Huge, Lomir Flamefist, Smaaash, Wardrummer, Charette, Drumble, Shooler, The Terror, Dr. Escotera, Dysania, Harland Mindlock, Skippy timehog, Timetraveller, Yxili Maurader, Horseman of *, Lady Maxena, Numquid the Fair, Raiding Knight, Sergeant Zakiel, Gatekeeper, Veemos Lightbringer, Magda, Old Bruno, Sneklifter, Urchin, Chota, Flaxia, Fuxxy Gruen, Lupo the Scarred, Mighty Tiger.
The Play ability only happens once. When restriguntus is Played, it sets "your opponent" to be the universal constant of the "your opponent" at the time you played the card. That constant does not change just because ownership of the creature changes; The play ability does not trigger again, so nothing changes.
Imagine "Your opponent" is a placeholder for your opponent's actual name... say it's Bob. I play Restringuntus: "Play: Choose a house. Bob cannot choose that house as their active house until Restringuntus leaves play." That is set and done. Bob takes control of Resty, the effect in play still says "Bob cannot choose that as their active house" because nothing triggered a change (Play ability is done)