Vegetable oil is almost always soybean oil. They mean vegetable in the “animal, vegetable, or mineral” sense, not in the “leafy green vegetable” sense. In other words, they mean oil that doesn’t come from an animal.
FTR, peanuts are around 48% oil (by weight). If you want to see it for yourself, throw a bunch of shelled and roasted peanuts (maybe a little salt) in your food processor and process until smooth. Let it sit for a few hours and watch the oil rise to the top. Or, buy some “natural” peanut butter (the kind that doesn’t contain hydrogenated oils in it). The ingredients list will usually just say “peanuts” and the jar will have a layer of oil sitting on top of the peanut butter.