They used to have a cheesesteak stand on the Boardwalk, but it closed. No reason it couldn't be done again if they wanted to.
As for the 'can't install grills because of the rooms above' case, there are ways around that - there are thousands of restaurants around the country with residential units directly above that can still prepare traditional grill type foods - there are ventless hood systems that run smoke and grease through multi-stage filters and can be paired with induction grills that produce less smoke and grease, and self-contained ventless grills like EVent that capture grease and smoke. Combined with convection ovens and fast-cook ovens like Turbo Chef which can cook chicken, steak, flatbreads, wings, etc., and self-contained fryer systems like PerfectFry for french fries, onion rings, mozz sticks, and tots, there's no reason they couldn't put a regular burger/diner/quick serve in that spot.