If he was convicted of assaulting his wife or had a DD both disqualifies him from owning a gun.
If he purchased the guns from a licensed dealer it is the states fault for not denying the purchase when his background check was performed.
The State of Texas does not require a background check. That is a
federal requirement.
If the perp bought the rifle from a private seller, that would circumvent the intent to keep wife-beaters from buying weapons. But if he bought it from a licensed dealer, there should have been a background check.
Let's talk about the dumbass form that is used to initiate the background check - I'm too lazy to look up the number right now.
It's a series of questions for the purchaser that asks things like "Are you a fugitive from justice?"
That's federal law for you.