Yall are correct in saying that Texas doesn't have a registry. I also know that our purchases are tracked a little differently if we buy multiple handguns or rifles larger than 22 cal at once or withing 5 days of each other. This records go to the atf and chief LEO in your jurisdiction. The CLEO id mandated to destroy those records within 20 days if you are found to be a nonprohibbited person. I don't know what the atf does with those records but I bet they are kept for a few lifetimes. They say its to track illegal gun trafficking. The rifle tracking is new since 2011 and only in California, Arizona, New Mexico, and Texas. I am on their lists. I have purchased several guns at once, several times. They did say that receivers are not tracked this way because they are neither rifle nor pistol.
The only rifles.22 caliber or larger rifles that must be reported in Texas are of the often misidentified so called assault weapons and only if more than one is purchased within 5 business days of each other at the same dealer. If you buy them at other dealers ATF doesn't know about them.