I assume the memory beam that he activated out of sequence still imparted the ability to understand and speak the language of the local natives.
Maybe it was the same type of technology that was used in another TOS episode.
The technology, that pumped knowledge into the brains of McCoy and that airhead gal in "Spock's Brain", might be similar to how the obelisk imparted knowledge of the native language into Kirk's brain.
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"The Paradise Syndrome" is a second rate episode, imo. But there is a wacky twist in the story that, for me, actually adds an interesting extra layer of context to the episode. It has nothing to do with Kirk's newfound language skill, though.
During TOS, Kirk proved himself to be, among other things, a slayer of false gods. He destroyed machines that had delusions of godhood, so to speak, like Landru and Vaal. He deposed flesh and blood gods, as well, like Apollo and Gary Mitchell, the friend who developed god complex.
In "The Paradise Syndrome", the tables were turned. It was Kirk who was put on a pedestal. Kirk, or Kirok, was a god to those Native American villagers.
Being a god came with perks, and Kirk made the most of his god status. For one thing, Kirk surely got to enjoy Miramanee.
But Kirk was a false god. And you know what happens to false gods.
Granted, Kirk had amnesia. He didn't know any better. And as Kirok, he did seem to mean well.
Nevertheless, Kirk got a taste of his own bitter medicine. The jeolous village medicine man eventually saw through Kirok's facade of godliness. And when the opportunity arose, he brutally exposed Kirk as a false god. Othe villagers saw the fraud, as well, when Kirk failed to stop the incoming storm. So, they stoned him.
It was Kirk's turn to be toppled from a godly perch. Poetic justice? What a bitter irony for Kirk.
Don't get me wrong. I am not suggesting that the writers had this in mind when they wrote this episode. Then again, maybe they did.
Anyway, when I view "The Paradise Syndrome" with the perspective that I described above, it makes, what is an otherwise mediocre episode, into something so much more watchable.