My take, as a layman, would be a business whose primary occupation is to dispense alcohol, bar, strip club, etc is off limits even if they serve a little food on the side.
A restaurant that is in the business to sell food that also has a bar area would be OK, as long as you were not actually sitting at the bar consuming alcohol.
Now, here is a personal observation - I was part of a function that took place in the parking lot of our American Legion Post. A FHP officer was there as part of the function. I needed to use the rest room, approached the officer, told him that I needed to go inside the post, but because I was carrying and there is a bar in there, was there a problem? He said no, the Post bar is private and it was OK.
I think the law is a little vague to allow common sense interpretation.