As egg layers, all dinosaurs were brooders, providing parental care. With a tepid climate, protection rather than warmth was what eggs needed to hatch. Like modern reptiles, dinosaurs were largely precocial.
Dinosaurs lived on Earth 180 million years; as a dominant group for ~140 million years. While fierce carnivores are the most celebrated, most dinosaurs were herbivores.
Dominion is a dramatic word. Certainly, dinosaurs excluded other vertebrates from proliferating as large animals.
Mammals are the most obvious example of this, but many other animals came along before the 1st dinosaur took a breath, and those other animals are still around.
Consider the cockroach, which debuted 360 MYA, during the Carboniferous (the earliest dinosaurs: 245 MYA). The cockroach thrives today, largely unchanged, except for a somewhat deteriorated diet owing to the evolution of fast-food restaurants.
As to dominion, microbes have ruled the world since they made the scene at the beginning of life, back before dirt was young. The power of the smallest life can never be overstated.
Viruses have the ability to manipulate the life histories and evolution of their hosts. ~ American virologists Forest Rohwer & Rebecca Vega Thurber