Actually, if he is an older stallion, he might not have had DNA filed at the time he was registered, but might have a bloodtype on file instead.
While it is true that AHA now requires DNA on file for both parents for a purebred
Arabian foal to be registered, unless something has changed in the last 4-5 years, they did not require DNA for the purebred parent to be on file for registering half
Regardless, even with a purebred foal it is NEVER too late to file DNA on a parent--- as long as the DNA GETS filed, you can register the offspring once its filed (the fees are high, but it can be done.) On previously bloodtyped Arabians, DNA SHOULD be filed before breeding takes place, but if it isn't, AHA allows you to "play catch up"-- at a price of course