No, as regular animals exist in the Pokemon world, too. The original games had cats and dogs in some houses. The cartoon showed non Pokemon birds flying alongside pidgeys and such.
The original games also made the claim that Pokemon came from space. They only showed up after a meteorite.
Which part? That Pokemon came from space or the inclusion of common animals like dogs and cats? I didn’t even know the show continued beyond my high school years until I saw all the talk about the show finally ending recently so I personally have no idea what they changed but the recent games I have played make the origin of the pokemon more mystical.
As far as I’m aware, the inclusion of real-world animal species in the older anime and games was due to the lack of variety in existing Pokemon species. The last time I know they referred to a real animal was in 2016, where the Pokedex entry for Raichu says it can knock out an Indian elephant. More recently, Raichu’s Pokedex entry was updated to instead say it can incapacitate a Copperajah.