I'd have done more with the Providers in this episode had I a hand in creating it. They seemed to warrant a bit more imagination than three brains with colors of the rainbow. More like the Organians who actually try to do something constructive in an earlier episode.
As it is these three are pretty powerful wired up as they are to all kinds of computer gadgetry. Out of sheer boredom they kidnap various alien humanoid species from across the galaxy and train them as Thrals which is their word for gladiators. They aren't sexist, they like their women warriors too.
So for new warriors when William Shatner, Nichelle Nichols, and Walter Koenig go on an away mission in the transporter they're snatched mid transport and dropped light years away on a barren planet where the Providers provide for the feeding and training and other creature comforts of their Thrals and then wager their bogus currency on who lives and dies.
I guess the Thrals are above humanoids, but below Organians in the evolutionary stage. In any event Kirk appeals to their sporting instinct to get out of this predicament.
Kirk is provided one shapely trainer in Angelique Pettyjohn. But for those of us with different tastes I certainly envied who Uhura gets in Steve Sandor. My screams would have been for joy.