I believe they do ship directly to your home, unless you are in a restricted state (which DE will soon be). I have a Garand on order, so I will know soon for sure.
From their FAQ:
Do rifles need to be shipped to a Licensed Dealer?
IMPORTANT: If your State or locality requires you to first obtain a license, permit, or Firearms Owner ID card in order to possess or receive a rifle, you must enclose a photocopy of your license, permit, or card with the application for purchase. Rifle shipments to NY, NJ and CT must be made to a state licensed dealer. You must provide a copy of the dealer’s license with your order form.
NY, NJ and CT customers who have already mailed their rifle orders to CMP should provide custserve@thecmp.org with dealer information or order cancellation instructions. Information can also be faxed to 256-835-3527 or mailed to CMP Customer Service, (Attn: FFL Order), 1401 Commerce Blvd., Anniston, AL 36207.