Three members of the Enterprise are transported light years away to perform in martial combat for all-powerful "brains".
A story that is cliched from the beginning, plenty of episodes dealt more effectively with the idea of humans faced with more powerful beings. Maybe most insulting is Kirk's willingness to engage romantically with his "Drill Thrall" at the same time that he states at the end that she is too unintelligent to travel to the stars. The script is not rising above the lowest of stereotypes here. Of all the Kirk romancing "green women" (or green-haired in this case), this one may be the most poorly-written.
Its also pretty far-fetched that the ultra-advanced Gamesters of Triskelion really think that wagers on combat and slavery have any intellectual value - even some comic books of the time were more sophisticated in examining the topic. The idea that Kirk would risk his crew on his final battle is totally without believablity as well. Shatner was in good shape for this episode, so he goes shirtless for a lot of scenes. But does the story really say anything about life in future centuries? Not really, its more 60s formulaic schlock.
I suppose that one positive aspect of the installment is using an Andorian as one of the captured Thralls, a bit of series continuity. But despite the violins first introduced in "Metamorphosis" playing in the background, this episode is really shallow in its script and ultimate impression on the viewer.