Actually, I believe they're Psychic-types. They may have another type as well, but my Alakazam attempted to speak with them telepathically. That isn't something he normally does to non-Psychic-types. In fact, he doesn't usually like any Pokémon who aren't Psychic-types. Of course it is possible that I'm mistaken, but I've had Alekhine for three years and his behavior hasn't changed at all in that time.

[So unless his Alakazam is tricking him (again), they're probably Psychic kitties. Which is pretty much Archer's ideal Pokémon.]