Psychic DO exist in the Fallout Universe, but they are VERY rare. The four psykers and The Master were psykers, and The Master was specially powerful. Try going though the Corridor of Revulsion without any protection. By the time you reach the Master, you will be pretty weakened by the Psychic attacks.
I think Psychic powers in the Fallout Universe are less flashy and more intricate. Illusions, hallucinations, mind reading, mental control, memory alternarion and maybe minor telekinesis. The Beastmasters were mutated by continuous exposure to radiation near their caverns, which made them able to control most animals with simple brains - Except humans and Deathclaws, who were smart and had brains complex enough to be immune to their attacks.