Well, some Pokémon in the anime don't chant their names over and over again. They're rather animalistic at times, but I wouldn't say it was taken directly from the games. But really, if you want to hear Pokémon have cries close to the games, or as rather realistic as possible, the Stadium games and the like are the way to go. In which case, if they had those actual cries in the anime, it'd be pretty neat to hear, but it wouldn't be "cute" enough. The Japanese gotta have their cute things, and what better way than to have Pikachus hop up and down chirping, "Pika pika pikachu!"?