If the shop or food location isn't owned by Disney, you cannot use a Disney gift card for payment, e.g. Crystal Arts/Arribas in DL, Ghirardelli's in DCA, non-Disney places in DTD.
If it is owned/operated by Disney and accepts credit cards you can use gift cards including DTD and the Resort Hotels. For example you can use your Gift Cards at the Starbucks in DL and DCA because they are operated by Disney but not at the the Starbucks in DTD because it is a Starbucks Corporate store.
Most of the DTD stores and restaurants however are third party operators thus Gifts Cards are not valid at.