It doesn't sound like a fine, which would be the result of the criminal case.
This sounds like a civil case--as suggested by the "Civil Demand" language--and it comes from Wal-Mart directly, probably exercising it rights under a state retail theft law.
There are two ways to skin this cat. You could just pay the $250. Or you could consult with a local criminal defense attorney--this isn't a criminal case, but they are the lawyers who are going to know about the retail theft laws--and asking whether the claim is legitimate under Kentucky law. I suspect that it probably is. Which means that your son is likely to have to pay something. It'd probably be cheaper to just pay the $250 than try to fight it. If you don't have the money, your son's wages will likely be garnished.
This answer does not constitute legal advice and does not establish an attorney-client relationship.