I don't know that I agree with that definition. I never cook vegetables before adding them to soups. At least once or twice a week I make a soup with onion/leek/spring onion, carrot, daikon radish, fresh chili, fresh ginger, fresh garlic, and noodles. Everything is cut fresh and cooked in the liquid for half an hour or longer before eating, and there is definitely not much liquid left since the noodles soak most of it up, but there's no way I'd call that a stew. In fact, I've never heard the word "stew" used for anything not containing meat, almost always beef with potatoes.
I do agree that something called a "stew" is more solid than liquid, like gulash. But I think the word really only applies to certain types of food. And certainly a soup is not necessarily something where the food was cooked first and added to the liquid after. I've never made soup that way. There are also things like squash/pumpkin soup, where the vegetables are boiled for a long time then the result is blended to give it a thick consistency without any chunks.
Actually, according to Wikipedia, it's food cooked in liquid for a long time over low heat and served with that liquid, like gravy, and it usually contains the least tender cuts of meat (toughest, containing the most fat) so it's best for long, slow cooking. In fact, it sounds like the definition of gulash. On the other hand, it says soup is made by boiling solid ingredients in a pot until the flavors are extracted - essentially the same thing as "stew" but without the note on it being servable on a plate. I think it comes down more to the types of ingredients used and the ratio of solid to liquid, though even something more solid than liquid could be called soup depending on what's in it.