Sen yai (wide fresh rice noodles) are the reason. They come pre oiled so they do not stick, and then they hit a wok with another ladle of oil, and their flat surface soaks it up. 200g of wide noodles is about 300 calories before cooking and closer to 420 after. That is the whole difference between pad see ew at 679 and rad na at 397, which uses the same noodles but in a starch gravy instead of fried.
The dark soy sauce is sweet soy, so there is sugar in there too, about 8 to 10g per plate. Together with the egg and pork it is a fatty, sweet, salty plate, which is exactly why it tastes so good at 11pm. The Chinese kale is the only free ingredient and there is usually only 40g of it.
It is not a bad plate of food, it is a big one. 24g of protein and 82g of carbs is a proper meal and then some. The way to eat pad see ew is as the meal, on its own, with nothing else. As a shared side dish next to a fried rice and a curry, which is how it turns up on a lot of tables, it is 680 calories that nobody is counting.