Are there any legal issues here? Aren't these chefs acting as a restaurant and wouldn't they need a license?
Indeed there are. Our chefs have business licenses, ServSafe certification, and food reseller permits. Regardless of legality, there are food safety issues. I wrote about how the traditional peer to peer doesn't work for food: http://blog.munchery.com/2011/11/pro-to-peer-a-new-paradigm/
I've always thought the game changer in this field would be based around bulk orders (group buying) - e.g., cheaper curry dish for you if others in your office or immediate area group together to improve scale efficiency for the chef and delivery.