They do it this way. From their website:
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"Buying a Firearm Online is Easy!
Add your selected firearm(s) to your shopping cart and check out.
Select a local Federal Firearms Licensed (FFL) Dealer that will accept the firearm and complete the transfer. Find a FFL Dealer HERE.
If you choose an FFL Dealer that is not on our preferred list, you or your FFL Dealer will be required to fax or email us a signed copy of the Federal Firearms License referencing your Cheaper Than Dirt! order number. Pick up your firearm from the FFL Dealer, who will need to do a background check. Transfer fees may apply. Buying Firearms on the Internet Federal law requires firearms to be shipped to FFL Dealers. For an individual to receive a firearm from Cheaper Than Dirt! it must be shipped to an FFL Dealer in your state.
Locating a Federal-Firearm License Dealer (FFL) in Your Area There are thousands of FFL Dealers in the United States. You may choose an FFL Dealer from our preferred listing or you may find a dealer in your area. To find a list of FFL Dealers in your area area CLICK HERE. If you choose a dealer that is not on our preferred list, either you or the FFL Dealer will be required to submit a copy of the Federal Firearms License referencing your Cheaper Than Dirt! order number. The FFL Dealer will usually charge a fee to conduct the transfer. There are duties that the FFL Dealer is required to do during the process which include a background check. Remember, the FFL Dealer is doing you a favor and the process takes time to complete. Fees can vary so check with the FFL Dealer ahead of time to request a quote on the fees associated with your firearm transfer. The FFL Dealer is in business to make a profit and your internet purchase may be viewed as competition to their retail business. If you feel the fees are too high, you can search for another FFL Dealer.
Completing the Transaction
Once you place the firearm in your cart and checkout you will receive a confirmation email that has your order number and further instructions. We will verify the FFL license and also make the FFL Dealer aware that an order from Cheaper Than Dirt! will soon be arriving for you. Most orders are processed within 2-3 business days from the time we receive and verify the FFL Dealers information. Once shipped, your firearm will arrive at the FFL Dealer within 3-7 days business days. The FFL Dealer will begin processing the shipment. It may be an additional day or so before the FFL Dealer is ready to conduct the transfer of the firearm to you. Call the FFL Dealer and set an appointment to confirm that the firearm is ready to be transferred. "
Thank you. This information helps. I’m wondering, though. Are there states which did not (prior to this incident) permit this type of transaction for firearms?