Not necessarily. The crunchy rice is from a specific way of serving it in a hot stone bowl, called dolsot bibimbap. IMHO, the main thing about bibimbap generally is (a) a bed of rice with (b) several toppings in smaller amounts and (c) a soft egg that creates a creamy sauce when stirred. That being said, "bibimbap" literally means "mixed rice", so it's a really variable thing, and the variety is a big part of it.