Horizon didn't have transporters. Kirk stated to Bela that he would explain the concept of the transporter after he beamed down.
Kirk also felt the need to explain "galaxies" and "lightspeed limits". It doesn't sound as if he had a good grasp of what the Iotians might or might not know.
Yes, Iotians are smart. And probably technologically highly advanced, in order to kick up an imitation of prohibition-era Chicago out of "beginnings of industrialization". Everything they do or say is make-believe, including all the parts where they play dumb: it takes major smarts to plausibly imitate a dimwitted 1920s henchman!
The Republic had an atomic matter pile. This was the old name for a type of nuclear reactor.
And torpedo was the old name for a bomb on a stick...
I rather think that the very use of the term "atomic matter pile" in the episode is the best proof that it refers to something as completely unrelated to the Chicago experiment as the photon torpedo is to the primary weapon of the good old Hunley