Someone correct me if I'm wrong, but, you can carry in Krogers and such due to the fact that they don't serve ON the premises.
-now, if they do wine tasting or something like that, I'm not sure how that'd work.
It is my understanding that places like Krogers and other regular businesses can post the 'no carry signs' (the ones with the X'ed out gun), but you can essentially ignore those. Only thing they can do if they catch you doing that is ask you to leave. I think where you can get into trouble is carrying where the .gov tells you that you can't carry. ie. bars.
I'm thinking that the sign you have posted is the wrong sign. If it's a Giant Eagle, Kroger, etc., then they should have the 'please don't carry here' sign, instead of the one you see now.