Let's see how many games we can think of that have the option to let you play as a dinosaur, whether it's the main character, a bonus, whatever.
Here's a few to start things off:
Dino City (SNES)
Bronkie the Bronchiasaurus (SNES) - A Raya Systems game about asthma
Jurassic Park (Genesis) - You can play as a Raptor, which imo is the best feature in the game.