The main reasons to cook food is to kill bacteria and increase nutritional value.
But what is “cooking”? From a biology perspective, it’s the denaturation of proteins and lysis of cells in your food. There are many ways to denature a protein: heat, acid (IE: Ceviche, cooked by the lime juice), enzymes (IE: papaya contains meat tenderizers)… All of these methods are indeed ways to “cook” food.
99 Celsius will denature proteins almost identically to 100 Celsius. Bringing the water to a boil might create steam inside of cells, forcing them to lyse. This will have a much weaker effect on what you consider “cooking” than the temperature will, but could make a small difference, particularly in plant cells that are resistant to lysis because of their tough cell walls.
This is exactly why it is more nutritionally beneficial to steam your vegetables than to boil them. When the cells do lyse, all of the contents get distributed among the boiling water solution, not in the cooked vegetable food you ultimately eat. Steamed veggies, on the other hand, may also have lysed cells, but the surrounding water vapor is much less efficient at leeching the contents out than was the liquid. There are exceptions to the rule: sweet potatoes are more healthy if boiled if you don’t add something like oil after steaming.
Boiling is simply the hottest water temperature you can achieve under current atmospheric conditions. Typically, when cooking food by submerging it in a non-oil liquid, there is no danger of burning the food, so the highest available temperature is preferred because it will yield the shortest cooking time. This is why most boiled food products, such as pastas, have high altitude instructions, which are usually as simple as “boil an extra few minutes.” The lower atmospheric pressure experienced at higher altitudes means water boils at lower temperatures, so you need to cook it longer.
There’s some debate about whether the definition of cooking is appropriate for things like pasta, bread, and legumes.
TLDR: temperature matters, not the change of state from a liquid to gas.