How does adding one ingredient to a dish prevent another from burning?

There is only one way that adding an ingredient prevents another one from burning: it brings down the temperature.

Usually this is because the added ingredient has a lot of moisture in it. Boiling off water, whether that water is in liquid or inside an ingredient like onions, requires a lot of heat energy, and while the water is being boiled off, the temperature of the cooking vessel drops towards 100C.

That's the case with the ginger in that recipe; ginger has water in it, and that water has to steam off, and will lower the oil temperature. However, since the ginger doesn't have much mass, it won't lower it very much or for very long ... which is why the chef adds the sliced potatoes less than 30 seconds later. The potatoes also have a lot of water, and they have a lot more mass.

Sometimes the ingredient will also lower the temperature because it is cold, and is being added to a cooking vessel with the heat turned off. A common example of this is adding cold butter to finish a sauce.

Now, sometimes online chefs will tell you "add X to prevent Y from burning" wholly inaccurately. If the added ingredient doesn't follow one or both of the criteria above, they're talking nonsense.

While FuzzyChef describes a correct mechanism, it does not apply to your video. You can stop peppercorns from burning if you drop, say, a can of tomatoes on them, but not by adding a teaspoon of ginger. You will also note that the next sentence in the video tells you to "quickly move on to stop these from burning too", the ginger clearly does not have enough thermal mass to stop the mixture from burning.

What is going on here is either sloppy language, or a misunderstanding of what is actually happening. Lots of chefs know what works, but not every one understands why it works.

The simple explanation is that food needs time in the hot pan to burn. And it is the total time spent there that counts, from adding to the pan, to the temperature going down through adding a sufficient mass of cold food. Adding the ginger does not stop the peppercorns from burning; moving on with the recipe quickly means that the peppercorns have not yet had time to burn by the time the temperature goes down.

There is a slight deviation from this in wokking, but this is not what we see in this video. With a wok, you add the new food to the small middle spot, to cook it quickly over high heat, while pushing the last batch of ingredients up the oblique walls, where it is at a temperature sufficient to continue cooking, but not enough to burn. In your video, the dish has not reached that stage, and the spices are all in the middle still.