Cooking (in the English I was taught) involves the application of heat - frying, baking, roasting, boiling etc are the names for specific ways to do this. A sandwich would be made or prepared.
Just for the heck of it, if you heat protein enough to denature it but have no Maillard reaction (let's say you've just made a hard boiled egg), would that not be considered cooking by that definition?
My understanding is that denaturing is a physical structure change, not a chemical one (and according to Wikipedia can be reversible in some cases), not a biochemist or food scientist though so totally accepting that my understanding is incorrect/incomplete.