Ironically, the main taxonomic difference between dinosaurs and other reptiles is that dinosaurs had their legs all the way underneath themnote , while other reptiles have their legs splayed out. Given that most dragons have their legs all the way underneath them, almost all dragons are taxonomically dinosaurs. In the Draconomicon for Dungeons and Dragons, it even specifically states that dragon legs are underneath their body instead of splayed out like most reptiles. Of course, because Our Dragons Are Different, this can vary from media to media, and dragons with splayed out limbs are not unknown. Additionally, they would have to be a different type of dinosaur than is currently known as almost all dragons are depicted as carnivorous. By comparison the only dinosaur group confirmed to contain carnivores, theropods, are virtually all exclusively bipedal.
It is also worth noting that this trope is highly reliant on pop cultural ideas of what dinosaurs were like, instead of the actual animals as they are known to be in reality. So Artistic License – Paleontology is going to very strongly factor. To most of the general public, dinosaurs were big, scaly, horned and spiky, brutish monsters that represent a bygone time; something that closely aligns with the Here There Were Dragons trope as many people's ideas of dragons set them in a historic age like Medieval times. In reality, dinosaurs ranged in size from gigantic to positively tiny, only some bore horns and spines and virtually none of the carnivorous ones had either, many times could be just as feathered as they were scaly; and were no more or less brutal or intelligent than most modern animals. Essentially, popular consciousness tends to portray dinosaurs as monsters instead of animals, so they can easily align with arguably the most famous monster archetype in fiction quite easily in such a scenario.
