Yes, they would, if the family spent less at Disney's Kings Island during the year than they would have spent on their WDW vacation. The average WDW guest pays a lot more per day than the average Kings Island guest, and most guests don't spend even 7 days at regional amusement parks. Consider that a DIS vacation for a family of 4 costs ~$2000 plus gas/airfare and food, and KI season passes for 4 is <$350 (2 adults + 2 children, or 4 adults in the fall).
That's apples to oranges. You are comparing a vacation to a season pass. Hundreds of thousands of guests would still flock to WDW and DL every year. I bet D.K.I. wouldn't hurt their bottom line, if not help it. There would be more repeat customers who would spend money on each trip.
Also Disney does not make money off any airfare. The airline makes that money. Also some people go off property to eat dinner.