You will need to explore the provided link further to get the list of specific restaurants that participate; not all do, and none of the cart vendors do. Here is the current list....
Disneyland® Park
* Rancho del Zocalo Restaurante
* Redd Rockett's Pizza Port
* Café Orleans
* Blue Ribbon Bakery
* Gibson Girl Ice Cream Parlor
Disney's California Adventure® Park
* Ariel's Grotto
* Cocina Cucamonga Mexican Grill
* Taste Pilots' Grill
* Schmoozie's
Disney's Grand Californian Hotel® & Spa
* Napa Rose
* Storytellers Café
* White Water Snacks
Disneyland® Hotel
* Goofy's Kitchen
* Hook's Pointe
* The Lost Bar
* Steakhouse 55
Disney's Paradise Pier® Hotel
* Disney's PCH Grill
To take the OP's question one step further.....say I have 200 points to redeem, & we dine at a restaurant such as Wine Country Trattoria, which offers a discount to Disney Visa cardholders. Can I still get the discount if I am not actually paying with the Disney Visa CREDIT card? Has anyone done this? I'm thinking of using our points towards a WOC dining package in November, but will spend the points on something else we had planned if the dining discount will be lost.