If it's a world like Pokemon you seek, something like Google Glass + AR generated Pokemon/battlefields shared between multiple people anyone? I honestly think that could happen in the near future.
If you disregard things like psychic and ghost types, the ability to communicate with humans, legendaries controlling nature, flashy attacks and the technology of the Pokemon world (none of which, besides communication, can exist naturally), it's pretty much Earth TBH.
Very nice reply what you said does make sense. But a parallel universe might have different laws of psychics that allow for all of this (just my view).