Looks like you should be able to earn 5% plus 5%.
This if copied from Discover's website:
ShopDiscover Terms & Disclosure
Cardmembers who participate in a Cashback Bonus Program will receive the specified Cashback Bonus on ShopDiscover purchases made with your Discover Card in connection with these promotions during valid promotion dates in addition to any other Cashback Bonus you will earn on that purchase. We are not responsible for merchant delays in processing transactions. Promotional reward will be applied within 8 weeks. See Terms and Conditions for full details. Offer valid only when you link to retailer site from the ShopDiscover Web page found at Discovercard.com and use your Discover Card. These offers are not valid in combination with any other offers. These offers are subject to change, including termination without notice. Cashback Bonus is not eligible on returned items purchased through ShopDiscover. Offer is not valid in combination with any other offers found outside of ShopDiscover.
And while Target Gift Cards and eGift Cards are excluded, it didn't list other Gift Cards as excluded from the 5% through Discover's portal.