What is 'Cooking Chorizo'?
Spanish Chorizo comes in two forms both of which to the best of my knowledge are fully cured (cooked):  one which is more for eating on its own (like salami) and the other which tends to have a higher ratio of fat in it and is used primarily for cooking.  The latter one being what the recipe is referring to as "cooking chorizo".  Oftentimes the cooking chorizo is in a paper casing that must be removed (unless you need some extra fiber in your diet).  Either one of these would work, however you might need to add a little oil to the pan if you need to cook other things in the fat that would normally be rendered out.

Mexican chorizo is always a raw product which must be cooked and is usually in a plastic casing.