Most species of animals in the wild would quickly be replaced as Pokémon can compete better for resources.
For humans the whole economic system would change:
>Businesses replace machine capital with Pokémom exploitation, similar to agricultural times of animal labour and slavery except at an industrial scale. Pokémon won't have rights at first so they'll be exploited quite a lot
>Most of Pokémon exploitation is using them as energy source, because they are incredibly efficient at it. Just a normal food intake for a regular sized monster can turn into powerful electric, heat, magnetic, kinetic, etc sources. Water pokémon can expulse more water than would fit in their bodies, etc.
>The transport system worldwide gets obsolete. Teleport is used everywhere. Entire roads, airports, ports get abandoned.
>Several jobs disappear, unemployment increases, people protest in the streets. Simultaneously new jobs related to Pokémon are created, like breeders, veterinaries, trainers.. Having Pokémon skills is valuable in the job market
>New religions are born based on Pokémon mythology and spirituality, Pokémon also change the way we understand the world and our relation with nature and the cosmos
>People with skills at training Pokémon get tremendous economic and political power. Using Metagross or Porygon to hack servers, get private information, sell it, get government secrets, etc
>All this chaos will prompt governments to regulate Pokémon ownership soon after the initial crisis happens. Owning Pokémon soon requires a license and passing a test where you prove your mental sanity, your economic ability to raise it and your good intentions. Every single pokémon you get must be registered on a public list. Some pokémon are simply prohibited to own, and so is teaching certain moves that are deemed too dangerous like earthquake. Since the governments won't be able to control everyone a huge black market develops with unregulated Pokémon traffic.