Officially, there are no animals in the Pokemon anime-verse, only Pokemon and humans. And before you start on how you totally saw several non-Pokemon animals (and a very convincing cow costume), Shudo would remind you that every bird or cat in the series was drawn against his wishes, and is therefore non-canon.
But since the Pokedex describes Pikachu as a "mouse" Pokemon and Meowth as a "scratch cat," he couldn't pretend they never existed at all. So on his personal blog, Shudo offered a compromise: All the animals did exist once, but then they conveniently went extinct. A message he wanted to reinforce, in perfectly sane fashion, with an episode wherein Pokemon trainers battle the reanimated skeleton of a Tyrannosaurus Rex.
So how does Shudo explain what happened to the non-monstrous critters? You'd think they were just Darwin-ed out of existence by Pokemon (mouse vs. mouse that shoots 100,000 volts out of its cheeks isn't exactly a fair fight), but that doesn't seem to be the case. Instead, Shudo wrote that some people still have old photographs of animals, meaning they managed to live side by side with their superpowered counterparts from the prehistoric age until sometime after we invented the camera. I
f anything, that makes their mysterious fate even more disturbing. Not only was their extinction a shockingly recent event, but every single animal went the way of the dodo in a matter of decades. Is there an undiscovered Pokemon out there who knows the move "Extinction-Level Event"? If so, it is clearly super effective.