From the article, it appears that his crime doesn't count since he was a minor. If true, then that's the problem--not guns.
I believe the pertinent statute here is 18 USC 922.
That's Federal law, not Arkansas.
The Brady bunch are, as usual, being disingenuous (and that's being polite-) by stating that there's nothing in *Arkansas* law to prohibit him from purchasing a firearm.