{As per Pokémon canon I think it’s safe to assume most Nintendo products and associated games exist in world- For Pokémon games specifically in world, think of them as like. Sports games!
While specifically titles like “Pokémon Red” might exist in universe as fictionilized versions of a famous champions journey, that kind of thing is far and few between as I think quite a few Current champions would sue (or at least others would on their behalf.)
Stuff like Pokémon Stadium, Pokkén and the mystery dungeon games is probably the norm as far as it goes for Pokémon games- Maybe a famous trainer or two licenses their likeness to be used as a npc battler, much like a real athelete would for a sports game.
As far as other games go? I don’t think Sonic or other animalian folks would be nessecarily “Pokemanified”- You have pokédex entries reffering to various Pokémon as “Cat”, “Dog” or “Bird” pokemon- While they don’t exist in forms that we recognise as irl creatures, I think terms like “Hedgehog” are still around as broader categories of classification.
In the pokemon world, “Sonic the hedgehog” is simply a reference to that broader classification- Like how you might have something labled as a “Canine” in fiction without really explaining in specifics. when you do get down to specifics, like say, a black bear- We make up fake animals all the time for video games! Why not in the pokemon world too?
All that being said, I think theoretically speaking, any video game could exist if it made sense- especially if it was funnier for it to do so }