A-2 are intended for food and/or drink (which this is) and also fits neatly into the "Restaurants, cafeterias, and similar dining facilities"
A-5 is for "participating in or viewing outdoor activities". You could say that eating and drinking is an activity, and that you are outdoors because you don't have walls.
302.1 says that where a structure is proposed for a purpose that is not specifically listed in this section, such a structure shall be classified in the group that the occupancy most nearly resembles, according to fire safety and relative hazard.
I started typing this post to say that this structure most nearly resembles an A-2, but upon reading 302.1 I realized that while this picnic area certainly resembles a restaurant, by only considering the fire safety and relative hazard of each occupancy, I think you are closer to an A-5 if there are no walls to obstruct egress and prevent the dissipation of smoke.
That is my opinion.