Psychic and Wyrm are oddities since they were added later in the game's life. (Like Fairy for Pokemon.) If Jinzo was made when Psychics were a thing, I could even see him having it.
Clefable, Gardevoir, Azumarill and many others actually changed Type after the introcution of the new one in the 6th Generation: KONAMI could have easily done something similar with Jinzo.