Yes. The use of the ATF Firearms Transaction Record, or Form 4473, is required by federal law for every Federal Firearms Licensee (gun store owner). It is a way for the government to make sure that each gun store is doing its due diligence to prevent guns from ending up in the hands of criminals. It is not a registration or a database, just think of it as a liability waiver.
The part you can skip is the accompanying FBI background check. That should save you some time after filling out your form.
For more information, see our article on “Do I have to register my gun?”