The way I see it is, a fist fight turning into shooting is rarely if ever justified. I don't know Arkansas current gun laws, but I suspect it likely makes any type of concealed carry while drunk, a crime, even with a permit.
So while this law loosens where someone is allowed to carry, it doesn't change the general CCW rule that you can't carry while drinking alcohol. And in turn, it doesn't justify anyone who escalates a fist fight into a shooting.