Would dinosaurs be still around if whatever caused its extinction 65 mya never happened?

Nothing's guaranteed, but I'd guess it's pretty likely that the non-avian dinosaurs would still be around somewhere. Compared to the amount of time that they were the dominant land animals on Earth, and the environmental changes they weathered in that time, 65 million years isn't a whole lot. The fact that the avian dinosaurs are still here may or may not be interesting to you. If the non-avians did survive to the present day (or close to it), the world would be a very different place. One could make the argument that their extinction was the factor that released the mammals to radiate into the dinosaurian niches. Without that mammalian radiation and wild-eyed evolution, it seems awfully unlikely that we would be here discussing the question..