Hello inflation.
Hello unemployment and more businesses leaving NY.
Exactly right. Not only are costs of menu items going up because of the minimum-pay workers, but all the way up the chain. The guy already making $15/hr will demand more. So will the next guy up the chain, now making $18/hr will want more. The ripple effect will cascade up who knows how far, and businesses will go nuts trying to please their workers, yet try to keep costs under control lest they go out of business.
Every time a business raises prices, they lose customers. In time, those customers may drift back; but maybe they won't. Many businesses will be in turmoil and will close their doors.
Because of higher prices, I don't bother frequenting fast food outlets. I stopped going some 10 to 15 years ago. I'll go to diners or nice restaurants where the prices reflect good food and ambiance. New York is nuts to do this socialist experiment doomed to failure; failure because low-wage workers will now become unemployable.